Use power series operations to find the Taylor series at x=0 for the following function. (5x^2)/2-5+5cosx.

pancha3 2020-11-29 Answered
Use power series operations to find the Taylor series at x=0 for the following function.
5x225+5cosx.
You can still ask an expert for help

Expert Community at Your Service

  • Live experts 24/7
  • Questions are typically answered in as fast as 30 minutes
  • Personalized clear answers
Learn more

Solve your problem for the price of one coffee

  • Available 24/7
  • Math expert for every subject
  • Pay only if we can solve it
Ask Question

Expert Answer

Alara Mccarthy
Answered 2020-11-30 Author has 85 answers
Two Taylor series at x=0 can be added term by term, giving rise to another Taylor series. The radius of convergence is going to be the minimum of the radii of convergence of the two (Taylor) power series. In our case, the term (5x225) is already a Taylor series at x=0. The Taylor series for cosxcosx at x=0 is given by
1x22!+x44!x66!++(1)nx2n(2n)!+
Adding term by term the two Taylor series, we get:
(5+1)+(5212)x2+x44!=x66!++(1)nx2n(2n)!+
which is equal to
4+2x2+x44!x66!++(1)nx2n(2n)!+
Not exactly what you’re looking for?
Ask My Question

Expert Community at Your Service

  • Live experts 24/7
  • Questions are typically answered in as fast as 30 minutes
  • Personalized clear answers
Learn more

Relevant Questions

asked 2021-01-28
Use the definition of Taylor series to find the Taylor series, centered at c, for the function. f(x)=cosx, c=π4
asked 2020-10-19
a) Find the Maclaurin series for the function
f(x)=11+x
b) Use differentiation of power series and the result of part a) to find the Maclaurin series for the function
g(x)=1(x+1)2
c) Use differentiation of power series and the result of part b) to find the Maclaurin series for the function
h(x)=1(x+1)3
d) Find the sum of the series
n=3n(n1)2n
This is a Taylor series problem, I understand parts a - c but I do not understand how to do part d where the answer is 72
asked 2022-02-24
How to get the sum of the series
n=11(4n21)2 ?
asked 2021-11-13
Show how to approximate the required work by a Riemann sum. Then express the work as an integral and evaluate it. A circular swimming pool has a diameter of 24 ft, the sides are 5 ft high, and the depth of the water is 4 ft. How much work is required to pump all of the water out over the side? (Use the fact that water weighs 62.5lb/ft^3.)
asked 2022-01-19
How can we prove that?
n=1x3n(3n1)!=13ex2x(e3x22sin(π+33x6))
asked 2021-02-06
Consider the following convergent series.
a. Find an upper bound for the remainder in terms of n.
b. Find how many terms are needed to ensure that the remainder is less than 103.
c. Find lower and upper bounds (ln and Un, respectively) on the exact value of the series.
k=113k
asked 2022-01-22
Prove that :
k=0(1)k(2k+1)3=π332