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‎01_limits/1.9_continuity/Untitled.ipynb‎

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{
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"cells": [
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{
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"cell_type": "markdown",
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"id": "b80020cc-6d89-442e-a99d-ce14c9837543",
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"metadata": {},
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"source": [
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"### **Problem 12**\n",
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"\n",
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"12\\. Determine where the following function is discontinuous.\n",
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"\n",
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"$$\n",
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"g(x) = \\tan(2x)\n",
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"$$"
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]
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},
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{
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"cell_type": "code",
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"execution_count": null,
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"id": "9a75c18c-1b4e-4d78-aa12-9ac78793d096",
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"metadata": {},
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"outputs": [],
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"source": []
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}
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],
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"metadata": {
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"kernelspec": {
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"display_name": "Python 3 (ipykernel)",
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"language": "python",
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"name": "python3"
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},
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"language_info": {
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"codemirror_mode": {
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"name": "ipython",
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"version": 3
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},
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"file_extension": ".py",
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"mimetype": "text/x-python",
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"name": "python",
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"nbconvert_exporter": "python",
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"pygments_lexer": "ipython3",
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"version": "3.12.6"
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}
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},
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"nbformat": 4,
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"nbformat_minor": 5
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}

‎01_limits/1.9_continuity/problem_03.ipynb‎

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{
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"cells": [
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{
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"cell_type": "markdown",
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"id": "d15e6440-e1b6-436d-bad9-5a9d1c57dec7",
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"metadata": {},
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"source": [
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"### **Problem**\n",
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"\n",
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"Using only Properties 1- 9 from the Limit Properties section, one-sided limit properties (if needed) and the definition of continuity determine if the following function is continuous or discontinuous at (a) $z = -1$, (b) $z = 0$, (c) $z = 3$?\n",
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"\n",
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"$$\n",
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"ry - 248\n",
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"$$"
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]
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},
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{
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"cell_type": "code",
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"execution_count": null,
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"id": "fff49d03-f74e-4ae8-979e-9b75c6a02e40",
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"metadata": {},
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"outputs": [],
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"source": []
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}
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],
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"metadata": {
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"kernelspec": {
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"display_name": "Python 3 (ipykernel)",
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"language": "python",
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"name": "python3"
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},
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"language_info": {
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"codemirror_mode": {
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"name": "ipython",
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"version": 3
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},
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"file_extension": ".py",
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"mimetype": "text/x-python",
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"name": "python",
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"nbconvert_exporter": "python",
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"pygments_lexer": "ipython3",
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"version": "3.12.6"
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}
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},
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"nbformat": 4,
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"nbformat_minor": 5
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}

‎01_limits/1.9_continuity/problem_04.ipynb‎

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{
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"cells": [
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{
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"cell_type": "markdown",
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"id": "f2045b8e-2ca4-434f-9d5f-5ab27a70f606",
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"metadata": {},
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"source": [
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"### **Problems**\n",
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"\n",
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"Using only Properties 1- 9 from the Limit Properties section, one-sided limit properties (if needed) and the definition of continuity determine if the following function is continuous or discontinuous at (a) $z = -2$, (b) $z = 0$, (c) $z = 5$?\n",
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"\n",
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"$$\n",
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"g(z) = 3 - 3z\n",
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"$$"
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]
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},
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{
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"cell_type": "code",
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"execution_count": null,
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"id": "b0e94c51-b50f-48a8-abf9-b03345c48d31",
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"metadata": {},
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"outputs": [],
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"source": []
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}
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],
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"metadata": {
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"kernelspec": {
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"display_name": "Python 3 (ipykernel)",
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"language": "python",
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"name": "python3"
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},
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"language_info": {
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"codemirror_mode": {
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"name": "ipython",
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"version": 3
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},
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"file_extension": ".py",
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"mimetype": "text/x-python",
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"name": "python",
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"nbconvert_exporter": "python",
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"pygments_lexer": "ipython3",
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"version": "3.12.6"
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}
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},
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"nbformat": 4,
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"nbformat_minor": 5
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}

‎01_limits/1.9_continuity/problem_05.ipynb‎

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{
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"cells": [
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{
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"cell_type": "markdown",
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"id": "4e164465-39f1-4d1d-9b21-7dd304142101",
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"metadata": {},
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"source": [
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"### **Problem**\n",
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"\n",
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"Using only Properties 1- 9 from the Limit Properties section, one-sided limit properties (if needed) and the definition of continuity determine if the following function is continuous or discontinuous at (a) $x = 4$, (b) $x = 6$?\n",
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"\n",
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"$$\n",
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"f(x) = \\begin{cases}\n",
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"x - 4 & \\text{if } x \\leq 6 \\\\\n",
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"I - x & \\text{if } x > 6\n",
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"\\end{cases}\n",
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"$$"
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]
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},
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{
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"cell_type": "code",
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"execution_count": null,
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"id": "4bbde048-c94e-48f3-a57a-c2d3dca871c0",
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"metadata": {},
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"outputs": [],
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"source": []
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}
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],
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"metadata": {
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"kernelspec": {
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"display_name": "Python 3 (ipykernel)",
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"language": "python",
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"name": "python3"
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},
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"language_info": {
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"codemirror_mode": {
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"name": "ipython",
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"version": 3
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},
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"file_extension": ".py",
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"mimetype": "text/x-python",
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"name": "python",
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"nbconvert_exporter": "python",
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"pygments_lexer": "ipython3",
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"version": "3.12.6"
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}
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},
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"nbformat": 4,
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"nbformat_minor": 5
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}

‎01_limits/1.9_continuity/problem_06.ipynb‎

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{
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"cells": [
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{
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"cell_type": "markdown",
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"id": "d9675773-5f18-4bf5-82f0-5697f7f7906b",
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"metadata": {},
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"source": [
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"### **Problem**\n",
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"\n",
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"Using only Properties 1- 9 from the Limit Properties section, one-sided limit properties (if needed) and the definition of continuity determine if the following function is continuous or discontinuous at (a) $t = -2$, (b) $t = 10$?\n",
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"\n",
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"$$\n",
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"h(t) = \\begin{cases}\n",
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"t^2 & \\text{if } t < -2 \\\\\n",
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"t + 6 & \\text{if } t > -2\n",
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"\\end{cases}\n",
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"$$"
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]
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},
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{
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"cell_type": "code",
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"execution_count": null,
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"id": "46ce1c78-9ba0-4098-b675-dd9411204d50",
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"metadata": {},
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"outputs": [],
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"source": []
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}
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],
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"metadata": {
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"kernelspec": {
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"display_name": "Python 3 (ipykernel)",
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"language": "python",
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"name": "python3"
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},
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"language_info": {
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"codemirror_mode": {
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"name": "ipython",
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"version": 3
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},
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"file_extension": ".py",
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"mimetype": "text/x-python",
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"name": "python",
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"nbconvert_exporter": "python",
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"pygments_lexer": "ipython3",
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"version": "3.12.6"
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}
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},
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"nbformat": 4,
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"nbformat_minor": 5
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}

‎01_limits/1.9_continuity/problem_07.ipynb‎

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{
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"cells": [
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{
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"cell_type": "markdown",
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"id": "4c39ade8-0a8a-4b2d-8813-2dfe246325dc",
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"metadata": {},
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"source": [
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"### **Problem**\n",
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"\n",
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"Using only Properties 1-9 from the Limit Properties section, one-sided limit properties (if needed) and the definition of continuity determine if the following function is continuous or discontinuous at (a) $x = -6$, (b) $x = 1$?\n",
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"\n",
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"$$\n",
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"g(x) =\n",
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"\\begin{cases}\n",
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"1 - 3x & x < -6 \\\\\n",
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"7 & x = -6 \\\\\n",
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"x^3 & -6 < x < 1 \\\\\n",
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"1 & x = 1 \\\\\n",
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"2 - x & x > 1\n",
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"\\end{cases}\n",
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"$$"
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]
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},
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{
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"cell_type": "code",
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"execution_count": null,
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"id": "2339ce02-9b01-4679-ae3d-c86eeb400ee3",
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"metadata": {},
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"outputs": [],
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"source": []
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}
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],
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"metadata": {
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"kernelspec": {
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"display_name": "Python 3 (ipykernel)",
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"language": "python",
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"name": "python3"
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},
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"language_info": {
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"codemirror_mode": {
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"name": "ipython",
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"version": 3
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},
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"file_extension": ".py",
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"mimetype": "text/x-python",
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"name": "python",
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"nbconvert_exporter": "python",
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"pygments_lexer": "ipython3",
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"version": "3.12.6"
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}
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},
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"nbformat": 4,
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"nbformat_minor": 5
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}

‎01_limits/1.9_continuity/problem_08.ipynb‎

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{
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"cells": [
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{
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"cell_type": "markdown",
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"id": "e6a14861-6dc9-4327-b1a8-55450b7c6a85",
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"metadata": {},
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"source": [
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"### **Problem**\n",
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"\n",
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"8\\. Determine where the following function is discontinuous.\n",
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"\n",
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"$$\n",
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"f(x) = \\frac{x^{2}-9}{3x^{2}+2x-8}\n",
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"$$"
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]
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},
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{
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"cell_type": "code",
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"execution_count": null,
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"id": "0fe6ad59-ba6f-465e-b5ed-53e5381867b1",
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"metadata": {},
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"outputs": [],
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"source": []
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}
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],
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"metadata": {
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"kernelspec": {
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"display_name": "Python 3 (ipykernel)",
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"language": "python",
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"name": "python3"
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},
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"language_info": {
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"codemirror_mode": {
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"name": "ipython",
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"version": 3
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},
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"file_extension": ".py",
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"mimetype": "text/x-python",
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"name": "python",
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"nbconvert_exporter": "python",
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"pygments_lexer": "ipython3",
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"version": "3.12.6"
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}
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},
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"nbformat": 4,
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"nbformat_minor": 5
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}

‎01_limits/1.9_continuity/problem_09.ipynb‎

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{
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"cells": [
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{
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"cell_type": "markdown",
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"id": "cc537118-addb-49a4-93e6-e8cad83531b5",
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"metadata": {},
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"source": [
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"### **Problem**\n",
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"\n",
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"Determine where the following function is discontinuous.\n",
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"\n",
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"$$\n",
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"f(t) = \\frac{8t}{t^2 - 9t-1}\n",
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"$$"
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]
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},
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{
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"cell_type": "code",
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"execution_count": null,
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"id": "ef74f784-78ea-4f36-bd19-d81b98769f40",
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"metadata": {},
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"outputs": [],
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"source": []
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}
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],
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"metadata": {
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"kernelspec": {
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"display_name": "Python 3 (ipykernel)",
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"language": "python",
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"name": "python3"
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},
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"language_info": {
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"codemirror_mode": {
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"name": "ipython",
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"version": 3
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},
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"file_extension": ".py",
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"mimetype": "text/x-python",
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"name": "python",
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"nbconvert_exporter": "python",
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"pygments_lexer": "ipython3",
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"version": "3.12.6"
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}
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},
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"nbformat": 4,
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"nbformat_minor": 5
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}

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