91Ó°ÊÓ

In Problems \(1-42,\) find the limits. $$ \lim _{\theta \rightarrow-\infty} \frac{\pi \theta^{5}}{\theta^{5}-5 \theta^{4}} $$

In Problems \(1-15,\) state whether the indicated function is continuous at \(3 .\) If it is not continuous, tell why. $$ g(t)=|t-2| $$

Evaluate each limit. $$ \lim _{\theta \rightarrow 0} \frac{\tan 5 \theta}{\sin 2 \theta} $$

In Problems \(1-42,\) find the limits. $$ \lim _{x \rightarrow \infty} \frac{3 x^{3}-x^{2}}{\pi x^{3}-5 x^{2}} $$

In Problems \(1-22,\) find the indicated limit or state that it does not exist. $$ \lim _{x \rightarrow 4} \frac{x-4}{\sqrt{x}-2} $$

In Problems \(7-10,\) plot the function \(f(x)\) over the interval [1.5,2.5] Zoom in on the graph of each function to determine how close \(x\) must be to 2 in order that \(f(x)\) is within 0.002 of \(4 .\) Your answer should be of the form "If \(x\) is within of _____ 2 , then \(f(x)\) is within 0.002 of \(4 . "\) $$ f(x)=\sqrt{8 x} $$

Evaluate each limit. $$ \lim _{\theta \rightarrow 0} \frac{\cot (\pi \theta) \sin \theta}{2 \sec \theta} $$

In Problems \(1-42,\) find the limits. $$ \lim _{\theta \rightarrow \infty} \frac{\sin ^{2} \theta}{\theta^{2}-5} $$

In Problems 7 - 18, find the indicated limit. In most cases, it will be wise to do some algebra first (see Example 2). $$ \lim _{x \rightarrow 0} \frac{x^{4}+2 x^{3}-x^{2}}{x^{2}} $$

In Problems \(1-15,\) state whether the indicated function is continuous at \(3 .\) If it is not continuous, tell why. $$ f(x)=\frac{21-7 x}{x-3} $$