Chapter 1: Problem 50
Finding a Limit What is the limit of \(g(x)=x\) as \(x\) approaches \(\pi ?\)
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Continuity on a closed Interval In Exercises 31-34, discuss the continuity of the function on the closed interval. $$ g(x)=\frac{1}{x^{2}-4} \quad \quad \quad[-1,2] $$
Making a Function Continuous In Exercises \(61-66,\) find the constant \(a,\) or the constants \(a\) and \(b\) , such the function is continuous on the entire real number line. $$ f(x)=\left\\{\begin{array}{ll}{3 x^{3},} & {x \leq 1} \\ {a x+5,} & {x>1}\end{array}\right. $$
Testing for Continuity In Exercises \(77-84\) , describe the interval(s) on which the function is continuous. $$ f(x)=\sec \frac{\pi x}{4} $$
Removable and Nonremovable Discontinuities In Exercises \(35-60,\) find the \(x\) -values (if any) at which \(f\) is not continuous. Which of the discontinuities are removable? \ $$ f(x)=x^{2}-9 $$
Continuity on a closed Interval In Exercises 31-34, discuss the continuity of the function on the closed interval. $$ \begin{array}{ll}{\text { Function }} & {\text { Interval }} \\\ {g(x)=\sqrt{49-x^{2}}} & {[-7,7]}\end{array} $$
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