Find the Maclaurin series for the function. (Use the table of power series for elementary functions.) \

$$g(x)=2 \sin x^3$$

Use a graphing utility to graph the first 10 terms of the sequence of partial sums and a horizontal line representing the sum.

$$\sum_{n=1}^{\infty} \frac{6}{n(n+3)}$$

Use a graphing utility to find the indicated partial sum $S_n$ and complete the table.

$$\sum_{n=1}^{\infty} \frac{6}{n(n+3)}$$

Find the sum of the series and its radius of convergence \

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

Use a computer algebra system to find the indicated Taylor polynomials for the function f. Graph the function and the Taylor polynomials.
$f(x)=\tan x$ \

$$n=3, \quad c=\pi / 4$$

Use a computer algebra system to find the indicated Taylor polynomials for the function f. Graph the function and the Taylor polynomials.
$f(x)=\tan x$
$n=3, \quad c=0$

Find the sum of the series.

$$\sum_{n=1}^{\infty} \frac{6}{n(n+3)}$$

Find the interval of convergence of the power series. (Be sure to include a check for convergence at the endpoints of the interval.)
$\sum_{n=0}^{\infty} \dfrac{x^{2 n+1}}{(2 n+1) !}$

Distance A ball is dropped from a height of 8 meters. Each time it drops h meters, it rebounds 0.7 h meters. Find the total distance traveled by the ball.

Find the limit (if possible) of the sequence. \

$$a_n=\dfrac{5 n^2}{n^2+2}$$

Find the Maclaurin series for the function. (Use the table of power series for elementary functions.) \

$$f(x)=\cos x^{3 / 2}$$

In this Exercise, (a) use Theorem discussed earlier to determine the number of terms required to approximate the sum of the convergent series with an error of less than $0.001$, and (b) use a graphing utility to approximate the sum of the series with an error of less than $0.001$.

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

Use Theorem discussed earlier to determine the convergence or divergence of the p-series.

$$\sum_{n=1}^{\infty} \frac{1}{n^{1.04}}$$

Use a graphing utility to approximate the sum of the series with an error of less than $0.001$.

$$\sum_{n=0}^{\infty} \frac{(-1)^n}{(2 n) !}=\cos 1$$