Chapter 1: Problem 6
Find the limit. $$ \lim _{x \rightarrow-3} \frac{2}{x+2} $$
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Give an example of two functions that agree at all but one point.
In Exercises \(25-34,\) find the limit. $$ \lim _{x \rightarrow 0^{+}} e^{-0.5 x} \sin x $$
In Exercises \(25-34,\) find the limit. $$ \lim _{x \rightarrow 0^{+}} \frac{2}{\sin x} $$
Prove that if \(\lim _{\Delta x \rightarrow 0} f(c+\Delta x)=f(c),\) then \(f\) is continuous at \(c\)
Use a graphing utility to graph the given function and the equations \(y=|x|\) and \(y=-|x|\) in the same viewing window. Using the graphs to visually observe the Squeeze Theorem, find \(\lim _{x \rightarrow 0} f(x)\). $$ h(x)=x \cos \frac{1}{x} $$
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