Calculus 2

Convert a rectangular equation, such as $x + y = 3$, to a polar equation.

Graph the polar equation $r = 2 \cos(\theta)$, and verify by converting to rectangular form.

Graph polar coordinates with given radius and angle.

Find the area of a circle using polar coordinates.

Graph the equation where $r = a \cos(2\theta)$.

Find the equation of the tangent line for the polar equation $r = 2 + 3\cos(\theta)$ when $\theta = \frac{\pi}{2}$.

Write the equation of the tangent line for the polar equation $r = 3 - 2\sin(\theta)$ when $\theta = \pi$.

Evaluate the double integral $\displaystyle \int_{0}^{2} \int_{-\frac{\pi}{2}}^{\frac{\pi}{2}} e^{-r^2} r \, dr \, d\theta$ by converting it to polar coordinates in the region bounded by $x = \sqrt{4 - y^2}$ and the y-axis.

Solve for y given $\frac{dy}{dx} = \frac{x^2}{y^2}$.

Solve for $y$ given $\frac{dy}{dx} = \frac{6x^2}{2y + \cos(y)}$.

dy/dx = x^2y. Solve for y.

dy/dx = xe$y$. Given the initial condition $y(0) = 0$, solve for $y$.

Solve the separable differential equation $\frac{dY}{dX} = -\frac{X}{Y}e^{X^2}$ given the initial condition that the solution must pass through the point (0,1).

Solve the differential equation: $\frac{dy}{dx} = x + x y^2$ with the initial condition $y(0) = -1$.

Solve the differential equation $x^2 + 1 \frac{dy}{dx} = x \cdot y$ by separating variables.

Verify that the solution to the exponential growth equation is $y = ce^{kt}$, where c is a constant.

Solve a first order differential equation using the method of separation of variables.

Solve the differential equation $y' = \frac{xy}{y^2 + 1}$ using separation of variables.

Solve the differential equation $\frac{dy}{dx} = 5x$.

Solve the differential equation $\frac{dy}{dx} = 3x^2 e^{-y}$ that satisfies the initial condition $y(0) = 0$.