Consider the function $z=e^x\cos \left(y\right)$. Which of the following best describes the domain of this function?

Let $g\left(x\right)={\int }_0^{x}f\left(t\right)dt$, where $f$ is the function whose graph is shown. Which of the following statements is true about $g\left(x\right)$?

Find the exact length of the curve given by $x=\frac{y^4}{8}+\frac{1}{4y^2}$, for $1\le y\le 3$.

Find the length of the curve given by $r\left(t\right)=(6t,t^2,\frac{t^3}{9})$ for $0\le t\le 1$.

Evaluate the iterated integral by converting to polar coordinates: $${\int }_0^2{\int }_{2-x^2}^{4-x^2}{x}^2+y^2 dy dx$$

For the function $f$ whose graph is given, which of the following best describes the domain of $f$?

Find the third-degree Taylor polynomial, $t_3\left(x\right)$, for the function $f\left(x\right)=\frac{1}{x}$ centered at $a=2$.

Given the polar curve $r=\cos \left(2\theta \right)$, what is the exact length of one petal of the curve?

Given the Laplace transform $F\left(s\right)=\frac{1}{s^2+1}$, find the corresponding function $f\left(t\right)$.