Calculus 2

Show that a parametric function tracing a curve can be re-parameterized to alter the rate at which the curve is traced without changing its shape.

Find the slope of the tangent line to a parameterized curve given functions $x(t)$ and $y(t)$.

Find the second derivative of a parameterized curve given functions $x(t)$ and $y(t)$.

Graph polar coordinates with given radius and angle.

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

For a series represented with a corresponding function over an interval, use the integral test to determine convergence.

Apply divergence test to a series where the sequence does not converge to zero, such as one involving logarithmic terms.

For series that resemble quotient forms, like $\frac{n}{n^3 + 1}$, determine convergence using the comparison or limit comparison test.

Attempt comparing series with non-standard terms using the limit comparison test.

Utilize the root test for series with terms that include powers like $(\text{something})^n$.

Apply the ratio test to series involving factorial terms and powers, such as those with $n!$ or similar structures.

If you look at the improper interval and the improper integral converges or diverges, whatever it does, the same is true of the series.