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<!DOCTYPE html><html><head><link rel="stylesheet" href="https://colbyn.github.io/school-notes/styling.8a512196.css"><script src="https://colbyn.github.io/school-notes/system.f84e1103.js"></script><script>window.MathJax={tex:{inlineMath:[["\\(","\\)"],["stem:[","]"]]},svg:{fontCache:"global"},processEscapes:!0};</script><script type="text/javascript" id="MathJax-script" async src="https://cdn.jsdelivr.net/npm/mathjax@3/es5/tex-svg.js">
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</header><script>function t(t,n){var a;if("undefined"==typeof Symbol||null==t[Symbol.iterator]){if(Array.isArray(t)||(a=e(t))||n&&t&&"number"==typeof t.length){a&&(t=a);var r=0,i=function(){};return{s:i,n:function(){return r>=t.length?{done:!0}:{done:!1,value:t[r++]}},e:function(t){throw t},f:i}}throw new TypeError("Invalid attempt to iterate non-iterable instance.\nIn order to be iterable, non-array objects must have a [Symbol.iterator]() method.")}var c,o=!0,h=!1;return{s:function(){a=t[Symbol.iterator]()},n:function(){var t=a.next();return o=t.done,t},e:function(t){h=!0,c=t},f:function(){try{o||null==a.return||a.return()}finally{if(h)throw c}}}}function e(t,e){if(t){if("string"==typeof t)return n(t,e);var a=Object.prototype.toString.call(t).slice(8,-1);return"Object"===a&&t.constructor&&(a=t.constructor.name),"Map"===a||"Set"===a?Array.from(t):"Arguments"===a||/^(?:Ui|I)nt(?:8|16|32)(?:Clamped)?Array$/.test(a)?n(t,e):void 0}}function n(t,e){(null==e||e>t.length)&&(e=t.length);for(var n=0,a=new Array(e);n<e;n++)a[n]=t[n];return a}function a(t){return t()}var r=[{name:"Homepage",path:"index.html"},{name:"Calculus 1",suffix:"Class Notes",path:"calc/index.html",sub:[{name:"Functions and Limits",chapter:"1",path:"calc/chapter1/index.html"},{name:"Derivatives",chapter:"2",path:"calc/chapter2/index.html"},{name:"Applications of Differentiation ",chapter:"3",path:"calc/chapter3/index.html"},{name:"Integrals",chapter:"4",path:"calc/chapter4/index.html"},{name:"Applications of Integration",chapter:"5",path:"calc/chapter5/index.html"},{name:"Inverse Functions",chapter:"6",path:"calc/chapter6/index.html"}]},{name:"Trigonometry",suffix:"Class Notes",path:"trig/index.html",sub:[{name:"Functions and Graphs",chapter:"1",path:"trig/chapter1/index.html"},{name:"Trigonometric Functions",chapter:"2",path:"trig/chapter2/index.html"},{name:"Trigonometric Identities and Equations",chapter:"3",path:"trig/chapter3/index.html"},{name:"Applications of Trigonometry",chapter:"4",path:"trig/chapter4/index.html"},{name:"Complex Numbers",chapter:"5",path:"trig/chapter5/index.html"},{name:"Topics in Analytic Geometry",chapter:"6",path:"trig/chapter6/index.html"},{name:"Exponential and Logarithmic Functions",chapter:"7",path:"trig/chapter6/index.html"}]}],i=window.location.host;function c(t){return"colbyn.github.io"===i?"https://colbyn.github.io/colbyns-math-notes/".concat(t):"/".concat(t)}function o(t){window.location.host;var e=document.createElement("li");return a(function(){var n=document.createElement("a");if(n.href=c(t.path),"suffix"in t){var a=document.createElement("span");a.className="suffix",a.textContent=t.suffix,n.appendChild(a)}if("chapter"in t){var r=document.createElement("span");r.className="chapter",r.textContent="Chapter ".concat(t.chapter),n.appendChild(r)}if("name"in t){var i=document.createElement("span");i.className="name",i.textContent=t.name,n.appendChild(i)}e.appendChild(n)}),"sub"in t&&e.appendChild(h(t.sub)),e}function h(e){var n,a=document.createElement("ul"),r=t(e);try{for(r.s();!(n=r.n()).done;)entry=n.value,a.appendChild(o(entry))}catch(i){r.e(i)}finally{r.f()}return a}var l=document.querySelector("header#root");console.assert(l),l.appendChild(h(r));</script> <h1>Chapter 1</h1><h2>§1.5 | The Limit of a Function</h2><section class="note-block block"><h1>Vertical Asymptote (Definition §1.5.6)</h1><p>The vertical line<span inline="" math-inline="">\(x = a\)</span>is called the **vertical asymptote** of the curve<span inline="" math-inline="">\(y = f(x)\)</span>if at least one of the following statements is true:</p><div block="" math-block="">$$ \begin{equation}
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\begin{split}
\lim_{x \to a} f(x) &= \infty \\
\lim_{x \to a} f(x) &= -\infty \\
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2 changes: 1 addition & 1 deletion docs/calc/chapter2/index.html
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<!DOCTYPE html><html><head><link rel="stylesheet" href="https://colbyn.github.io/school-notes/styling.8a512196.css"><script src="https://colbyn.github.io/school-notes/system.f84e1103.js"></script><script>window.MathJax={tex:{inlineMath:[["\\(","\\)"],["stem:[","]"]]},svg:{fontCache:"global"},processEscapes:!0};</script><script type="text/javascript" id="MathJax-script" async src="https://cdn.jsdelivr.net/npm/mathjax@3/es5/tex-svg.js">
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</header><script>function t(t,n){var a;if("undefined"==typeof Symbol||null==t[Symbol.iterator]){if(Array.isArray(t)||(a=e(t))||n&&t&&"number"==typeof t.length){a&&(t=a);var r=0,i=function(){};return{s:i,n:function(){return r>=t.length?{done:!0}:{done:!1,value:t[r++]}},e:function(t){throw t},f:i}}throw new TypeError("Invalid attempt to iterate non-iterable instance.\nIn order to be iterable, non-array objects must have a [Symbol.iterator]() method.")}var c,o=!0,h=!1;return{s:function(){a=t[Symbol.iterator]()},n:function(){var t=a.next();return o=t.done,t},e:function(t){h=!0,c=t},f:function(){try{o||null==a.return||a.return()}finally{if(h)throw c}}}}function e(t,e){if(t){if("string"==typeof t)return n(t,e);var a=Object.prototype.toString.call(t).slice(8,-1);return"Object"===a&&t.constructor&&(a=t.constructor.name),"Map"===a||"Set"===a?Array.from(t):"Arguments"===a||/^(?:Ui|I)nt(?:8|16|32)(?:Clamped)?Array$/.test(a)?n(t,e):void 0}}function n(t,e){(null==e||e>t.length)&&(e=t.length);for(var n=0,a=new Array(e);n<e;n++)a[n]=t[n];return a}function a(t){return t()}var r=[{name:"Homepage",path:"index.html"},{name:"Calculus 1",suffix:"Class Notes",path:"calc/index.html",sub:[{name:"Functions and Limits",chapter:"1",path:"calc/chapter1/index.html"},{name:"Derivatives",chapter:"2",path:"calc/chapter2/index.html"},{name:"Applications of Differentiation ",chapter:"3",path:"calc/chapter3/index.html"},{name:"Integrals",chapter:"4",path:"calc/chapter4/index.html"},{name:"Applications of Integration",chapter:"5",path:"calc/chapter5/index.html"},{name:"Inverse Functions",chapter:"6",path:"calc/chapter6/index.html"}]},{name:"Trigonometry",suffix:"Class Notes",path:"trig/index.html",sub:[{name:"Functions and Graphs",chapter:"1",path:"trig/chapter1/index.html"},{name:"Trigonometric Functions",chapter:"2",path:"trig/chapter2/index.html"},{name:"Trigonometric Identities and Equations",chapter:"3",path:"trig/chapter3/index.html"},{name:"Applications of Trigonometry",chapter:"4",path:"trig/chapter4/index.html"},{name:"Complex Numbers",chapter:"5",path:"trig/chapter5/index.html"},{name:"Topics in Analytic Geometry",chapter:"6",path:"trig/chapter6/index.html"},{name:"Exponential and Logarithmic Functions",chapter:"7",path:"trig/chapter6/index.html"}]}],i=window.location.host;function c(t){return"colbyn.github.io"===i?"https://colbyn.github.io/colbyns-math-notes/".concat(t):"/".concat(t)}function o(t){window.location.host;var e=document.createElement("li");return a(function(){var n=document.createElement("a");if(n.href=c(t.path),"suffix"in t){var a=document.createElement("span");a.className="suffix",a.textContent=t.suffix,n.appendChild(a)}if("chapter"in t){var r=document.createElement("span");r.className="chapter",r.textContent="Chapter ".concat(t.chapter),n.appendChild(r)}if("name"in t){var i=document.createElement("span");i.className="name",i.textContent=t.name,n.appendChild(i)}e.appendChild(n)}),"sub"in t&&e.appendChild(h(t.sub)),e}function h(e){var n,a=document.createElement("ul"),r=t(e);try{for(r.s();!(n=r.n()).done;)entry=n.value,a.appendChild(o(entry))}catch(i){r.e(i)}finally{r.f()}return a}var l=document.querySelector("header#root");console.assert(l),l.appendChild(h(r));</script> <h1>Chapter 2 | Derivatives</h1>
</header><script>function t(t,n){var a;if("undefined"==typeof Symbol||null==t[Symbol.iterator]){if(Array.isArray(t)||(a=e(t))||n&&t&&"number"==typeof t.length){a&&(t=a);var r=0,i=function(){};return{s:i,n:function(){return r>=t.length?{done:!0}:{done:!1,value:t[r++]}},e:function(t){throw t},f:i}}throw new TypeError("Invalid attempt to iterate non-iterable instance.\nIn order to be iterable, non-array objects must have a [Symbol.iterator]() method.")}var o,c=!0,h=!1;return{s:function(){a=t[Symbol.iterator]()},n:function(){var t=a.next();return c=t.done,t},e:function(t){h=!0,o=t},f:function(){try{c||null==a.return||a.return()}finally{if(h)throw o}}}}function e(t,e){if(t){if("string"==typeof t)return n(t,e);var a=Object.prototype.toString.call(t).slice(8,-1);return"Object"===a&&t.constructor&&(a=t.constructor.name),"Map"===a||"Set"===a?Array.from(t):"Arguments"===a||/^(?:Ui|I)nt(?:8|16|32)(?:Clamped)?Array$/.test(a)?n(t,e):void 0}}function n(t,e){(null==e||e>t.length)&&(e=t.length);for(var n=0,a=new Array(e);n<e;n++)a[n]=t[n];return a}function a(t){return t()}var r=[{name:"Homepage",path:"index.html"},{name:"Calculus 1",suffix:"Class Notes",path:"calc/index.html",sub:[{name:"Functions and Limits",chapter:"1",path:"calc/chapter1/index.html"},{name:"Derivatives",chapter:"2",path:"calc/chapter2/index.html"},{name:"Applications of Differentiation ",chapter:"3",path:"calc/chapter3/index.html"},{name:"Integrals",chapter:"4",path:"calc/chapter4/index.html"},{name:"Applications of Integration",chapter:"5",path:"calc/chapter5/index.html"},{name:"Inverse Functions",chapter:"6",path:"calc/chapter6/index.html"}]},{name:"Trigonometry",suffix:"Class Notes",path:"trig/index.html",sub:[{name:"Functions and Graphs",chapter:"1",path:"trig/chapter1/index.html"},{name:"Trigonometric Functions",chapter:"2",path:"trig/chapter2/index.html"},{name:"Trigonometric Identities and Equations",chapter:"3",path:"trig/chapter3/index.html"},{name:"Applications of Trigonometry",chapter:"4",path:"trig/chapter4/index.html"},{name:"Complex Numbers",chapter:"5",path:"trig/chapter5/index.html"},{name:"Topics in Analytic Geometry",chapter:"6",path:"trig/chapter6/index.html"},{name:"Exponential and Logarithmic Functions",chapter:"7",path:"trig/chapter6/index.html"}]}],i=window.location.host;function o(t){return"colbyn.github.io"===i?"https://colbyn.github.io/school-notes/".concat(t):"/".concat(t)}function c(t){window.location.host;var e=document.createElement("li");return a(function(){var n=document.createElement("a");if(n.href=o(t.path),"suffix"in t){var a=document.createElement("span");a.className="suffix",a.textContent=t.suffix,n.appendChild(a)}if("chapter"in t){var r=document.createElement("span");r.className="chapter",r.textContent="Chapter ".concat(t.chapter),n.appendChild(r)}if("name"in t){var i=document.createElement("span");i.className="name",i.textContent=t.name,n.appendChild(i)}e.appendChild(n)}),"sub"in t&&e.appendChild(h(t.sub)),e}function h(e){var n,a=document.createElement("ul"),r=t(e);try{for(r.s();!(n=r.n()).done;)entry=n.value,a.appendChild(c(entry))}catch(i){r.e(i)}finally{r.f()}return a}var l=document.querySelector("header#root");console.assert(l),l.appendChild(h(r));</script> <h1>Chapter 2 | Derivatives</h1>
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