In this task, use the Ratio Test to determine the convergence or divergence of the series.

$$\displaystyle\sum_{n=1}^{\infty} \frac{n^n}{n !}$$

Find the area of the region bounded by the graphs of y = 7/(16 - x²) and y = 1.

In this exercise, find the interval of convergence of the power series. (Be sure to include a check for convergence at the endpoints of the interval.)

$$\displaystyle\sum_{n=0}^{\infty} \frac{(-1)^n x^{2 n+1}}{2 n+1}$$

Use the definition of Taylor series to find the Taylor series, centered at for the function. f(x) = cos x, c=π/4

Use the definition of Taylor series to find the Taylor series, centered at c, for the function.

$$f(x)=\sqrt{x}, \quad c=4$$

State where the power series is centered. Σ_(n=0)^∞ (-1)^n (x-π)^2n / (2n)!

Find the nth Maclaurin polynomial for the function. f(x) = e^(-x), n=5

In this exercise, find the $n$th Taylor polynomial centered at $c$.

$$f(x)=\dfrac{2}{x^2}, \quad n=4, \quad c=2$$

Find the area of the described region. Enclosed by $r=6 \sin \theta$

Find the area of the circle given by $r=\sin \theta+\cos \theta$. Check your result by converting the polar equation to rectangular form, then using the formula for the area of a circle.

Write an integral that represents the area of the shaded region of the figure. r = cos 2θ

In this task, write the next two apparent terms of the sequence. Describe the pattern you used to find these terms.

$$\dfrac{7}{2}, 4, \dfrac{9}{2}, 5, \ldots$$

Find dy/dx and the slopes of the tangent lines shown on the graph of the polar equation. (5, π/2) (2, π) (-1, 3π/2). r = 2+3 sin θ

The rectangular coordinates of a point are given. Plot the point and find two sets of polar coordinates of the point for 0 ≤ θ < 2π. (-√3, -√3)