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Chapter 1: Problem 50
Finding a Limit What is the limit of \(g(x)=x\) as \(x\) approaches \(\pi ?\)
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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? \ $$ f(x)=\frac{|x+7|}{x+7} $$
Using the Intermediate Value Theorem In Exercises \(91-94,\) use the Intermediate Value Theorem and a graphing utility to approximate the zero of the function in the interval \([0,1] .\) Repeatedly "zoom in" on the graph of the function to approximate the zero accurate to two decimal places. Use the zero or root feature of the graphing utility to approximate the zero accurate to four decimal places. $$ f(x)=x^{4}-x^{2}+3 x-1 $$
True or False? In Exercises \(103-106,\) determine whether the statement is true or false. If it is false, explain why or give an example that shows it is false. If \(f(x)=g(x)\) for \(x \neq c\) and \(f(c) \neq g(c),\) then either \(f\) or \(g\) is not continuous at \(c .\)
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? \ $$ f(x)=\left\\{\begin{array}{ll}{\frac{1}{2} x+1,} & {x \leq 2} \\ {3-x} & {x>2}\end{array}\right. $$
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? \ $$ f(x)=\left\\{\begin{array}{ll}{\csc \frac{\pi x}{6},} & {|x-3| \leq 2} \\\ {2,} & {|x-3|>2}\end{array}\right. $$
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