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.

$\lim_{x\rarr0}x^3+5x^2-7x+3$

Find the limit.

$\lim_{x\rarr2}\sqrt{x^2+5}$

Find the limit.

$\lim_{x\rarr3}\frac{x^2+2x-3}{x-2}$

Find the limit.

$\lim_{x\rarr0}\frac{3x^2+7x}{x}$

Find the limit.

$\lim_{x\rarr2}\frac{x^2-7x+12}{x-3}$

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.

$\lim_{x\rarr3}\frac{\sqrt{x}-\sqrt3}{x-3}$

Find the limit.

$\lim_{x\rarr0}\frac{\sqrt{x+1}-1}{x}$

Find the limit.

$\lim_{x\rarr5}\frac{x-5}{\sqrt{x}-\sqrt5}$

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