Detailed Explanations for Calculus 2 Equations

Use the definition of Taylor series to find the Taylor series, centered at c, for the function. $f (x) = \cos x, c = \frac{- π}{4}$

Tammy Todd 2021-01-28

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

Brennan Flores 2021-01-27

Population y grows according to the equation $\frac{d y}{d t} = k y$ , where is k - constant and t is measured in years. Of the population doubles every ten years, then the value of k is ?

Ayaana Buck 2021-01-24

a. Another Maclaurin series we examined is for sin x: a. Find the series for $\frac{\sin (x^{2})}{x}$ . Express the result in the summation notation, not just as a partial listing of the series terms.
b. Another Maclaurin series we examined is for sin x:
d. Find the series for integral $\frac{\sin (x^{2})}{x}$

Reeves 2021-01-22

Find the Maclaurin series for the function $f (x) = \cos 4 x$ . Use the table of power series for elementary functions

snowlovelydayM 2021-01-19

Taylor series
a. Use the definition of a Taylor series to find the first four nonzero terms of the Taylor series for the given function centered at a.
b. Write the power series using summation notation.
$f (x) = 2^{x}, a = 1$

Wribreeminsl 2021-01-19

Find the sum of the series:
$\sum_{n = 0}^{\infty} ((\frac{5}{2^{n}}) - (\frac{1}{3^{n}}))$

alesterp 2021-01-19

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

opatovaL 2021-01-16

Does the series (showing the picture) converge or diverge?
Choose the correct answer below.
1) The integral test shows that the series converges
2) The nth-term test shows that the series converges
3) The series diverges because the series is a geometric series with $| r | >= 1$
4) The nth-term test shows that the series diverges
$\sum_{n = 1}^{\infty} \frac{4^{n}}{n + 1}$

Jaya Legge 2021-01-15

It is important to distinguish between
$\sum_{n = 1}^{\infty} n^{b} and \sum_{n = 1}^{\infty} b^{n}$
What name is given to the first series? To the second? For what values of b does the first series converge? For what values of b does the second series converge?

CheemnCatelvew 2021-01-13

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

Daniaal Sanchez 2021-01-13

A) Does this series converge? If yes, towards what number?
B) Find the first 5 terms of the sequence of partial sums in this series.
C) What is the general term of this sequence of partial sums?
$\sum_{k = 1}^{\infty} (\frac{2}{k} - \frac{2}{k + 1})$

Harlen Pritchard 2021-01-10

The problem question is:
$\frac{d y}{d t} = a y + b y^{2}$
we have to sketch the graph f(y) versus y, determine the critical points, and classify each one as asymptotically stable or unstable.Thing is, how do you get the critical points?

Burhan Hopper 2021-01-10

Use the Limit Comparison Test to prove convergence or divergence of the infinite series.
$\sum_{n = 1}^{\infty} \frac{e^{n} + n}{e^{2 n} - n^{2}}$

tabita57i 2021-01-08

Solve the initial value problem: $(\tan (y) - 2) d x + (x \sec^{2} (y) + \frac{1}{y}) d y = 0$ , $y (0) = 1$

a2linetagadaW 2021-01-08

Use a power series to test the series $\sum_{n = 1}^{\infty} n^{\log x}$ for convergence, where $\sum$ means summation

Bergen 2021-01-06

Find a formula for the nth partial sum of the series and use it to determine whether the series converges or diverges. If a series converges, find its sum.
$\sum_{n = 1}^{\infty} (\cos^{- 1} (\frac{1}{n + 1}) - \cos^{- 1} (\frac{1}{n + 2}))$

geduiwelh 2021-01-05

Find the series

shadsiei 2021-01-05

Confirm that the Integral Test can be applied to the series. Then use the Integral Test to determine the convergence or divergence of the series.
$\sum_{n = 1}^{\infty} 3^{- n}$

Clifland 2021-01-04

Does the attached series converge or diverge? Note: it is a complex series and not a real series. Ive

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