AP Calculus AB Unit 1: Limits and Continuity

Find $\underset{x\to \infty }{\lim }\frac{2x^2-5x+1}{3x^2+x-7}$.

The function $f(x)=\{\begin{array}{ll}{x}^2& x<1\\ ax+b& x\ge 1\end{array}$ is continuous and differentiable at $x=1$. What are $a$ and $b$?

If $f(x)=\frac{x^2-4}{x-2}$ for $x\ne 2$ and $f(2)=5$, then $f$ is:

If $\underset{x\to 4^{-}}{\lim }f(x)=5$ and $\underset{x\to 4^{+}}{\lim }f(x)=7$, then:

Evaluate $\underset{x\to 0}{\lim }\frac{\sin (3x)}{x}$.

Evaluate $\underset{x\to 3}{\lim }\frac{x^2-9}{x-3}$.

Evaluate $\underset{x\to 0}{\lim }\frac{1-\cos x}{x^2}$.

Apply the squeeze theorem to evaluate $\underset{x\to 0}{\lim }{x}^2\sin \left(\frac{1}{x}\right)$.