Detailed Explanations for Calculus 2 Equations

Using Maclaurin series, determine to exactly what value the following series converges:
$\sum_{n = 0}^{\infty} \frac{(\ln 5)^{n}}{n!}$

ka1leE 2021-01-02

$w = x \sin y, x = e^{t}, y = π - t$ , value $t = 0$ , find $\frac{d w}{d t}$ using the appropriate Chain Rule and evaluate $\frac{d w}{d t}$ at the given value of t.

DofotheroU 2021-01-02

Write out the first three nonzero terms of the Taylor series for the following functions centered at the given point a. Then write the series using summation notation.
$f (x) = \tan^{- 1} 4 x, a = 0$

kuCAu 2021-01-02

Find the interval of convergence of the power series.
$\sum_{n = 1}^{\infty} \frac{4^{n} (x - 1)^{n}}{n}$

boitshupoO 2020-12-31

(a) write the repeating decimal as a geometric series, and (b) write its sum as the ratio of two integers. $0. \overset{―}{81}$

Cheyanne Leigh 2020-12-30

Use Theorem Alternating Series remainder to determine the number of terms required to approximate the sum of the series with an error of less than 0.001.
$\sum_{n = 1}^{\infty} \frac{(- 1)^{n + 1}}{n^{5}}$

rocedwrp 2020-12-29

Taylor series Write out the first three nonzero terms of the Taylor series for the following functions centered at the given point a. Then write the series using summation notation.
$f (x) = cosh (2 x - 2), a = 1$

Lipossig 2020-12-28

Use the Direct Comparison Test or the Limit Comparison Test to determine the convergence or divergence of the series.
$\sum_{n = 1}^{\infty} \frac{1}{\sqrt{n^{3} + 2 n}}$

permaneceerc 2020-12-25

Determine whether the series converges or diverges and justify your answer. If the series converges, find its sum
$\sum_{n = 0}^{\infty} \frac{3^{n - 2}}{4^{n + 1}}$

texelaare 2020-12-21

Use the formula for the sum of a geometric series to find the sum or state that the series diverges (enter DIV for a divergent series).
$\sum_{n = 2}^{\infty} \frac{5^{n}}{12^{n}}$

Lipossig 2020-12-21

Determine the convergence or divergence of the series.
$\sum_{n = 1}^{\infty} \ln (\frac{n + 1}{n})$

sibuzwaW 2020-12-17

Determine the radius of convergence of this series.
$\sum_{n = 0}^{\infty} (- 1)^{n} \frac{x^{2 n + 1}}{2 n + 1}$

tinfoQ 2020-12-17

Find the Maclaurin series for using the definition of a Maclaurin series. [Suppose it has a power series expansion. Do not show that Rn(x) tends to 0.] Find the related radius of convergence as well. $f (x) = (1 - x)^{- 2}$

mattgondek4 2020-12-16

Use the Limit Comparison Test to determine the convergence or divergence of the series.
$\sum_{n = 1}^{\infty} \frac{5}{4^{n} + 1}$

Globokim8 2020-12-16

Find the gradient at the point (3,-3,2) of the scaler field given by $f = x y - 4 z e + 35$

Mylo O'Moore 2020-12-15

Find the sum of the convergent series.
$\sum_{n = 0}^{\infty} (- \frac{1}{5})^{n}$

BenoguigoliB 2020-12-15

Find the Taylor series centered at zero for the function $f (x) = \ln (2 + x^{2})$ . Determine the radius of convergence of this series.

bobbie71G 2020-12-13

Does the series $\sum_{n = 1}^{\infty} \frac{n + 5}{n \sqrt{n + 3}}$ converges of diverges

Kaycee Roche 2020-12-09

Determine the convergence or divergence of the series.
$\sum_{n = 1}^{\infty} (1 + \frac{1}{n})^{n}$

Reggie 2020-12-09

Find the Taylor series for f(x) centered at the given value of a. [Assume that f has a power series expansion.
$R_{n} (x) \to 0$
$f (x) = 2 \cos (x), a = 3 π$

When you are dealing with any Calculus 2 homework, it is vital to have a look at the various questions and answers that will help you see whether you are correct in your approach to finding solutions. Even if you are dealing with analytical aspects of Calculus 2, it will be helpful as you are looking at provided equations and learn how the answers relate to original questions and problems specified.

Do not be afraid to take a look at the basic integration and related application if Calculus 2 does not sound clear or start with the Calculus 1 first.

Calculus 2

Calculus 2 Equations: Expert Solutions and More