Worked examples – Limits

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Worked Examples – Limits The indeterminate forms of limits $ displaystyle infty cdot infty ,infty cdot 0,frac{infty }{infty },frac{0}{0},frac{infty }{0},infty +infty ,infty -infty {{,1}^{infty }}{{,0}^{infty }},{{infty }^{0}}$ The indeterminate forms of limits $displaystyle infty cdot infty ,infty cdot 0,frac{infty }{infty },frac{0}{0},frac{infty }{0},$ $displaystyle infty +infty ,infty -infty ,{{1}^{infty }},{{0}^{infty }},{{infty }^{0}}$ Important Limits $ displaystyle […]

Theorems on Limits

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Theorems on Limits It can be rather tedious to apply the $displaystyle varepsilon $ and $displaystyle delta $ limit test to individual functions. By remembering some basic theorems about limits we can avoid the some of this repetitive work. We shouldn’t forget that if a limit exists it is always unique.  “The Uniqueness of a Limit” […]

Introduction to Limits

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Introduction to Limits Numerical and Graphical approach to limits Numerical Approach Let’s take a function f(x) and see how the values of the functions change when x takes values closer to a specific number. Example: Let f(x)=3x+1 and calculate f(x) as x takes values closer to 1, but not exactly the value at 1. We first […]

The Limit of a Function

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The limit of a function Let f be a function and let c be a real number. We do not require that f be defined ar c but we do require that f be defined at least on a set of the form (c-p,c) U (c,c+p) with p>0). To say that $displaystyle underset{{xto c}}{mathop{{lim }}},f(x)=l$ is […]