How do I do this? 3. (a) Consider the following: Apply the Lagrange Remainder Theorem to the function f(x) = . sSOthatf(x) = 1 – x + x² –- x³ + ...+ (-1)^x^ + En(x)where(-1)N+1(1 +c)N+1 ®N+1for some c between 0 and x. If x = 1, then 0

Name: How do I do this? 3. (a) Consider the following: Apply the Lagrange Re
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Description: How do I do this? 3. (a) Consider the following: Apply the Lagrange Remainder Theorem to the function f(x) = . sSOthatf(x) = 1 – x + x² –- x³ + ...+ (-1)^x^ + En(x)where(-1)N+1(1 +c)N+1 ®N+1for some c between 0 and x. If x = 1, then 0

Given function is f(x)=11+x Also given that 11+x=1-x+x2-x3+...+(-1)nxn+En(x)

Math

Advanced Math

3. (a) Consider the following: Apply the Lagrange Remainder Theorem to the function f(x) = so that f(x) = 1– x + x² – x³ + · .+ (-1)NxN + EN (x) where (-1)N+1 (1+c)N+1® EN(x) for some c between 0 and x. If x = 1, then 0

3. (a) Consider the following: Apply the Lagrange Remainder Theorem to the function f(x) = so that f(x) = 1– x + x² – x³ + · .+ (-1)NxN + EN (x) where (-1)N+1 (1+c)N+1® EN(x) for some c between 0 and x. If x = 1, then 0

Algebra & Trigonometry with Analytic Geometry

13th Edition

ISBN:9781133382119

Author:Swokowski

Publisher:Swokowski

Chapter4: Polynomial And Rational Functions

Section4.3: Zeros Of Polynomials

Problem 3E

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Topic Video

Question

How do I do this?

3. (a) Consider the following: Apply the Lagrange Remainder Theorem to the function f(x) = . s
SO
that
f(x) = 1 – x + x² –
- x³ + ...+ (-1)^x^ + En(x)
where
(-1)N+1
(1 +c)N+1 ®N+1
for some c between 0 and x. If x = 1, then 0 <c<1 and |EN(1)|
EN(x) =
(1tN+I → 0 as n → 0. Is
(1+c
this correct? If not, explain what went wrong.
(b) We know that the series below converges. Do the theorems of Chapter 6 fully justify the assertion
about its value? Explain.
1
1
1
+ -
- + - - ...?
3
4
1
log(2)
= 1-

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