91Ó°ÊÓ

\(17-20\) Explain why the function is discontinuous at the given number \(a\) . Sketch the graph of the function. \(f(x)=\left\\{\begin{array}{ll}{e^{x}} & {\text { if } x<0} \\ {x^{2}} & {\text { if } x \geq 0}\end{array}\right. \quad a=0\)

Determine whether the sequence is convergent or divergent. If it is convergent, find the limit. \(a_{n}=\frac{n^{2}}{\sqrt{n^{3}+4 n}}\)

Evaluate the limit, if it exists. $$\lim _{x \rightarrow-2} \frac{x+2}{x^{3}+8}$$

\(5-28\) Find the limit. $$\lim _{x \rightarrow \infty}\left(\sqrt{9 x^{2}+x}-3 x\right)$$

Determine whether the sequence is convergent or divergent. If it is convergent, find the limit. \(a_{n}=\sin (n \pi / 2)\)

Explain why the function is discontinuous at the given number \(a\) . Sketch the graph of the function. \(f(x)=\left\\{\begin{array}{ll}{\frac{x^{2}-x}{x^{2}-1}} & {\text { if } x \neq 1} \\ {1} & {\text { if } x=1}\end{array}\right. \quad a=1\)

Evaluate the limit, if it exists. $$\lim _{h \rightarrow 0} \frac{\sqrt{1+h}-1}{h}$$

\(5-28\) Find the limit. $$\lim _{x \rightarrow \infty}\left(\sqrt{x^{2}+a x}-\sqrt{x^{2}+b x}\right)$$

Explain why the function is discontinuous at the given number \(a\) . Sketch the graph of the function. \(f(x)=\left\\{\begin{array}{ll}{\cos x} & {\text { if } x<0} \\ {0} & {\text { if } x=0} \\ {1-x^{2}} & {\text { if } x>0}\end{array}\right. \quad a=0\)

Determine whether the sequence is convergent or divergent. If it is convergent, find the limit. \(a_{n}=\cos (n \pi / 2)\)