Assume you invest \$250 at the end of each year for 10 years at an annual interest rate of $r$. The amount of money in your account after 10 years is given by $A\left(r\right)=\frac{250({(1+r)}^{10}-1)}{r}$. Assume your goal is to have \$3500 in your account after 10 years.


b. Use a calculator to estimate the interest rate required to reach your financial goal.

Find the vertical asymptotes. For each vertical asymptote x=a, analyze lim x→a^- f(x) and lim x→a⁺ f(x).

f(x) = (x^4−1)/(x^2−1)

Complete the following steps for the given functions. 

b. Find the vertical asymptotes of $f$ (if any).

$f\left(x\right)=\frac{x^2-3}{x+6}$

Let $g\(\left\)(x\(\right\))=\(\begin{cases}\)x^2+x & \(\text{if }\)x<1\\ a & \(\text{if }\)x=1\\ 3x+5 & \(\text{if }\)x>1\(\end{cases}\)$

b. Determine the value of $a$ for which $g$ is continuous from the right at $1$. 

The graph of f in the figure has vertical asymptotes at x=1 and x=2. Analyze the following limits. <IMAGE>

lim x→1^+ f(x)

Complete the following steps for the given functions. 

b. Find the vertical asymptotes of f (if any).

$f\left(x\right)=\frac{3x^2-2x+5}{3x+4}$

Graph the function f(x)=e^−x / x(x+2)^2 using a graphing utility. (Experiment with your choice of a graphing window.) Use your graph to determine the following limits.

b. lim x→−2 f(x)