Question
Asked Jun 6, 2019
177 views

at what points x in the interval (-1,1] can one use the Lagrange Remainder Theorem to verify the expansion log(1+x) = summation (-1)^k+1 *x^k*1/k!

check_circle

Expert Answer

Step 1

The LaGrange remainder theorem:

f (x) be a real valued function defined in I,

  1. i) f (x) has derivative in upon interval I.
  2. ii) f (x) is continuous in I.

Then there exists an element between x and a such that,

help_outline

Image Transcriptionclose

"(a)(x-a)R(x) f(x)=f(a)+f(a)(x-a)+£°(a)(x-a) + 2! n! Where R. (x)= * (x)(x-a)"* (n+1) n+1 f

fullscreen
Step 2

Here the given interval is (–1,1] which is at x = 0 and to verify the expansion.

help_outline

Image Transcriptionclose

log (1+x)- k!

fullscreen
Step 3

Obtain the derivative...

help_outline

Image Transcriptionclose

f (x)=log (1+x) 1 f(x) 1x -1 f(x) (1+x) 2 "(x)1x) -6 f"(x)1+x)

fullscreen

Want to see the full answer?

See Solution

Check out a sample Q&A here.

Want to see this answer and more?

Solutions are written by subject experts who are available 24/7. Questions are typically answered within 1 hour.*

See Solution
*Response times may vary by subject and question.
Tagged in

Math

Advanced Math