91Ó°ÊÓ

\(5-28\) Find the limit. $$\lim _{x \rightarrow \infty} \frac{6}{3+e^{-2 x}}$$

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

\(5-28\) Find the limit. $$\lim _{x \rightarrow \infty} \sqrt{x^{2}+1}$$

Explain why the function is discontinuous at the given number \(a\) . Sketch the graph of the function. \(f(x)=\left\\{\begin{array}{ll}{\frac{2 x^{2}-5 x-3}{x-3}} & {\text { if } x \neq 3} \\ {6} & {\text { if } x=3}\end{array}\right. \quad a=3\)

Evaluate the limit, if it exists. $$\lim _{x \rightarrow-1} \frac{x^{2}+2 x+1}{x^{4}-1}$$

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

Guess the value of the limit (if it exists) by evaluating the function at the given numbers (correct to six decimal places). $$\begin{array}{l}{\lim _{x \rightarrow-1} \frac{x^{2}-2 x}{x^{2}-x-2}} \\\ {x=0,-0.5,-0.9,-0.95,-0.99,-0.999} \\ {-2,-1.5,-1.1,-1.01,-1.001}\end{array} $$

Guess the value of the limit (if it exists) by evaluating the function at the given numbers (correct to six decimal places). \(\lim _{t \rightarrow 0} \frac{e^{5 t}-1}{t}, \quad t=\pm 0.5, \pm 0.1, \pm 0.01, \pm 0.001, \pm 0.0001\)

Evaluate the limit, if it exists. $$\lim _{x \rightarrow 16} \frac{4-\sqrt{x}}{16 x-x^{2}}$$

\(5-28\) Find the limit. $$\lim _{x \rightarrow \infty} \frac{x^{4}-3 x^{2}+x}{x^{3}-x+2}$$