1. Limits and Continuity

Assume lim x→1 f(x)=8,lim x→1 g(x)=3, and lim x→1 h(x)=2 Compute the following limits and state the limit laws used to justify your computations.

lim x→1 f(x) / g(x)−h(x)

Determine the following limits.

lim x→1 x^3 − 7x^2 + 12x / 4 − x

Even function limits Suppose f is an even function where lim x→1^− f(x)=5 and lim x→1^+ f(x)=6. Find lim x→−1^− f(x) and limx→−1^+ f(x).

Determine the following limits.

$\underset{z\to 4}{\lim }\frac{z-5}{{(z^2-10z+24)}^2}$

Determine the following limits.

$\underset{\theta \to 0^{-}}{\lim }\frac{\sin \theta }{{\cos }^2\theta -1}$

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.

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