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

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: $${\int }_0^2{\int }_{2-x^2}^{4-x^2}{x}^2+y^2 dy dx$$

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

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

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 $f\left(t\right)$.

Evaluate the line integral of the vector field $F(x,y)=(x+6y)dx+x^{2}dy$ along the curve $C$, where $C$ is the line segment from $(0,0)$ to $(2,1)$. Which of the following is the value of the integral?

Evaluate the line integral of the vector field $F(x,y)=(x+7y,x^2)$ along the curve $C$, where $C$ is the line segment from $(0,0)$ to $(1,2)$. Which of the following is the value of the integral ${\int }_C^{}(x+7y)dx+x^{2}dy$?