1
hard
Differential equations
Calculus
Find
\[
\mathcal{L}^{-1}\left(\frac{3s+8}{s^2+2s+5}\right).
\]
Sign in to see the solution.
2
warmup
Multivariable calculus
Calculus
Find the value of $\int_{C} (x+y)ds$, where $C$ is the curve parameterized by $x=t$, $y=t$, $0 \leq t \leq 1$.
Sign in to see the solution.
3
hard
Parametric equations and vector functions
Calculus
Region enclosed by one petal of $r=8 \sin (2\theta)$
Sign in to see the solution.
4
warmup
Parametric equations and vector functions
Calculus
$$3x^2 - 4y^2 = 12$$
Sign in to see the solution.
5
hard
Parametric equations and vector functions
Calculus
Region below the polar axis and enclosed by $r=1-\sin \theta$
Sign in to see the solution.
6
core
Parametric equations and vector functions
Calculus
\([T] Use a graphing utility and sketch the graph of
r = \frac{6}{2 \sin \theta - 3 \cos \theta}.\)
Sign in to see the solution.
7
warmup
Parametric equations and vector functions
Calculus
$$\frac{(x - 1)^2}{16} - \frac{(y + 2)^2}{9} = 1$$
Sign in to see the solution.
8
hard
Parametric equations and vector functions
Calculus
Region enclosed by $r=1-2 \cos \theta$ and outside the inner loop
Sign in to see the solution.
9
core
Parametric equations and vector functions
Calculus
Focus (0, 0.5) and directrix $y = -0.5$
Sign in to see the solution.
10
hard
Vector spaces
Linear algebra
\([T] \rho = 2 \cos \varphi\)
Sign in to see the solution.