Calculus 2

Graph the parametric equations $x=2t$ and $y=t^2$ by picking some $t$ values and finding the corresponding $x$ and $y$ values. Plot the points and connect them to see the resulting parabola.

Parametrize the unit circle in the XY-plane in XYZ space using trigonometry, with $R(T) = (\cos(T), \sin(T), 0)$ for T in $[0, 2\pi]$.

Parametrize the straight line segment from point P to point Q using $R(T) = (1-T) \cdot OP + T \cdot OQ$ for T in $[0,1]$.

Plot and identify the positions of three points given in polar coordinates.

Convert a point from polar to rectangular coordinates using trigonometry and Pythagorean theorem.

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

Graph polar coordinates with given radius and angle.

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

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

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

Determine if the infinite series of $2n$ will converge or diverge.

What is the sixth term of the arithmetic sequence if the first term is 3 and the common difference is 2?

Write a formula to find the 20th term of the arithmetic sequence where the first term is 3 and the common difference is 2.

Determine the fifth term of the geometric sequence where the first term is 5 and the common ratio is 3.

Calculate the sum of the first 10 terms of the geometric sequence where the first term is 5 and the common ratio is 3.

Find the sum of an infinite geometric series where the first term is 100 and the common ratio is $\frac{1}{2}$.

Write a rule for the arithmetic sequence given two terms: The third term is 7, and the fifth term is 13.

Using the summation notation $\Sigma$, calculate the sum of the arithmetic series from $k=1$ to $k=10$ with the arithmetic rule $a_k = 3k + 2$.

Find the sum of the infinite geometric series with first term $\frac{4}{27}$ and a common ratio of $\frac{1}{3}$.

Find out what a sequence does in the limit of $N\to\infty$ for the sequence A sub N equals N.