1. Limits and Continuity

Evaluate the limit, if it exists: $\underset{(x,y)\to (0,0)}{lim}\frac{xy}{x^2+y^2}$.

Given the function $f\left(x\right)=2x^2-3x+1$, which of the following is the average rate of change of $f\left(x\right)$ over the interval from $x=-6$ to $x=-3$?

Find the exact length of the curve $y=x-x^2+{\sin -1}^x$ from $x=0$ to $x=1$.

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

Which of the following is the correct algebraic method to find the limit $\underset{x\to 2}{lim}\frac{x^2-4}{x-2}$?

Find the exact length of the curve $y=\ln (\sec (x\left)\right)$ for $0\le x\le \frac{\pi }{4}$.