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Magazine Problem 43
Find the \(x\) -values (if any) at which \(f\) is not continuous. Which of the discontinuities are removable? $$ f(x)=\frac{|x+2|}{x+2} $$
Problem 43
Find the limit. \(\lim _{x \rightarrow 0^{+}} \frac{2}{\sin x}\)
Problem 43
Find the limit \(L\). Then use the \(\varepsilon-\delta\) definition to prove that the limit is \(L\). $$ \lim _{x \rightarrow 0} \sqrt[3]{x} $$
Problem 44
Find the \(x\) -values (if any) at which \(f\) is not continuous. Which of the discontinuities are removable? $$ f(x)=\frac{|x-3|}{x-3} $$
Problem 44
Find the limit. \(\lim _{x \rightarrow(\pi / 2)^{+}} \frac{-2}{\cos x}\)
Problem 44
Find the limit \(L\). Then use the \(\varepsilon-\delta\) definition to prove that the limit is \(L\). $$ \lim _{x \rightarrow 4} \sqrt{x} $$
Problem 45
Find the \(x\) -values (if any) at which \(f\) is not continuous. Which of the discontinuities are removable? $$ f(x)=\left\\{\begin{array}{ll} x, & x \leq 1 \\ x^{2}, & x>1 \end{array}\right. $$
Problem 45
Find the limit of the function (if it exists). Write a simpler function that agrees with the given function at all but one point. Use a graphing utility to confirm your result. $$ \lim _{x \rightarrow-1} \frac{x^{2}-1}{x+1} $$
Problem 45
Find the limit \(L\). Then use the \(\varepsilon-\delta\) definition to prove that the limit is \(L\). $$ \lim _{x \rightarrow-2}|x-2| $$
Problem 46
Find the \(x\) -values (if any) at which \(f\) is not continuous. Which of the discontinuities are removable? $$ f(x)=\left\\{\begin{array}{ll} -2 x+3, & x<1 \\ x^{2}, & x \geq 1 \end{array}\right. $$
