1. Limits and Continuity

Find the arc length of the graph of the function $y=\frac{2}{3}{x}^{\frac{3}{2}}+\frac{1}{3}$ over the interval $0\le x\le 9$.

Find the limit.

$\(\lim\)_{x\(\rarr\)0}x^3+5x^2-7x+3$

Find the limit.

$\(\lim\)_{x\(\rarr\)2}\(\sqrt{x^2+5}\)$

Find the limit.

$\(\lim\)_{x\(\rarr\)3}\(\frac{x^2+2x-3}{x-2}\)$

Find the limit.

$\(\lim\)_{x\(\rarr\)0}\(\frac{3x^2+7x}{x}\)$

Find the limit.

$\(\lim\)_{x\(\rarr\)2}\(\frac{x^2-7x+12}{x-3}\)$

Find the limit.

$\(\lim\)_{x\(\rarr\)-2}\(\frac{x^2-5x-14}{x+2}\)$

Find the limit.

$\(\lim\)_{x\(\rarr\)-\(\pi\)}\(\frac{\sin x}{x}\)$

Find the limit.

$\(\lim\)_{x\(\rarr\)3}\(\frac{\sqrt{x}\)-\(\sqrt\)3}{x-3}$

Find the limit.

$\(\lim\)_{x\(\rarr\)0}\(\frac{\sqrt{x+1}\)-1}{x}$

Find the limit.

$\(\lim\)_{x\(\rarr\)5}\(\frac{x-5}{\sqrt{x}\)-\(\sqrt\)5}$

Find the following limits or state that they do not exist. Assume a, b , c, and k are fixed real numbers.

lim h→0 √16 + h − 4 / h

Find the following limits or state that they do not exist. Assume a, b , c, and k are fixed real numbers.

lim x→4 1/x−1/4 / x − 4

Find the following limits or state that they do not exist. Assume a, b , c, and k are fixed real numbers.

lim h→0 (5 + h)^2 − 25 / h

Find the following limits or state that they do not exist. Assume a, b , c, and k are fixed real numbers.

lim x→4 3(x − 4)√x + 5 / 3 − √x + 5