The Maclaurin series for

aortiH
2021-02-02
Answered

Find the Maclaurin series for $f(x)={x}^{4}\mathrm{cos}x$ . Also, find the third term for this series.

The Maclaurin series for$\mathrm{cos}(x)$ is given by:

$\mathrm{cos}(x)=\sum _{n=0}^{\mathrm{\infty}}(-1{)}^{n}\frac{{x}^{2n}}{(2n)!}=1-\frac{{x}^{2}}{2!}+\frac{{x}^{4}}{4!}-\frac{{x}^{6}}{6!}+\frac{{x}^{8}}{8!}-\frac{{x}^{10}}{10!}+...$

The Maclaurin series for

You can still ask an expert for help

lamanocornudaW

Answered 2021-02-03
Author has **85** answers

The Maclaurin series for

Multiply the Maclaurin series for

Thus, the Maclaurin series for

Now find the third term for this series as shown below.

Hence, the third term of the series is

Jeffrey Jordon

Answered 2021-12-17
Author has **2262** answers

Answer is given below (on video)

asked 2022-04-28

Solve this nonhomegenous ode

$y{}^{\u2033}+4y=\mathrm{cos}\left(2x\right)$

asked 2021-09-12

Polar coordinates of point P are given. Find all of its polar coordinates.

asked 2022-02-26

Evaluate:

$\sum _{n=1}^{\mathrm{\infty}}\frac{{n}^{2}+1}{n\cdot {2}^{n-1}}$

asked 2022-07-17

How to get the proper maclaurin series representation for $\mathrm{cos}x$

asked 2022-04-19

What is a solution to the differential equation $\frac{dy}{dx}=\frac{2y+{x}^{2}}{x}$ ?

asked 2022-01-05

I really can't remember (if I have ever known this): which series is this and how to demonstrate its solution?

$\sum _{i=1}^{n}i=\frac{n(n+1)}{2}$

asked 2022-01-21

How to prove:

$\sum _{k=1}^{\mathrm{\infty}}\frac{k-1}{2k(1+k)(1+2k)}={\mathrm{log}}_{e}8-2$