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Magazine Problem 14
Finding a Limit In Exercises \(7-26\) , find the limit (if it exists). If it does not exist, explain why. $$ \lim _{x \rightarrow 10^{+}} \frac{|x-10|}{x-10} $$
Problem 14
Finding Vertical Asymptotes In Exercises \(13-28\) , find the vertical asymptotes (if any) of the graph of the function. $$ f(x)=\frac{2}{(x-3)^{3}} $$
Problem 14
Finding a Limit In Exercises \(5-22,\) find the limit. $$ \lim _{x \rightarrow 2} \sqrt[3]{12 x+3} $$
Problem 14
In Exercises 7鈥�14, create a table of values for the function and use the result to estimate the limit. Use a graphing utility to graph the function to confirm your result. $$ \lim _{x \rightarrow 0} \frac{\tan x}{\tan 2 x} $$
Problem 15
Finding Vertical Asymptotes In Exercises \(13-28\) , find the vertical asymptotes (if any) of the graph of the function. $$ f(x)=\frac{x^{2}}{x^{2}-4} $$
Problem 15
Finding a Limit In Exercises \(7-26\) , find the limit (if it exists). If it does not exist, explain why. $$ \lim _{\Delta x \rightarrow 0^{-}} \frac{\frac{1}{x+\Delta x}-\frac{1}{x}}{\Delta x} $$
Problem 15
Finding a Limit In Exercises \(5-22,\) find the limit. $$ \lim _{x \rightarrow-4}(x+3)^{2} $$
Problem 15
In Exercises 15鈥�22, use the graph to find the limit (if it exists). If the limit does not exist, explain why. $$ \lim _{x \rightarrow 3}(4-x) $$
Problem 16
Finding a Limit In Exercises \(5-22,\) find the limit. $$ \lim _{x \rightarrow 0}(3 x-2)^{4} $$
Problem 16
Finding a Limit In Exercises \(7-26\) , find the limit (if it exists). If it does not exist, explain why. $$ \lim _{\Delta x \rightarrow 0^{+}} \frac{(x+\Delta x)^{2}+x+\Delta x-\left(x^{2}+x\right)}{\Delta x} $$
