Answer is given BUT need full detailed steps andprocess since I don't understand the concept. 3. Use Taylor series expansions to determine the error in the approxima-tion u"(t) z u(t+3h)-3u(t+2h)+3u(t+h)-u(t)=u+3hu'+(36)e u!l+(34 "' (34)*-3 u&+26) =u+2hu' +24u fthl =uthulto243l a? u" ++ 13(6) +4" (36)num =24%3D4 Find AR which make the approimation

Answered: 3. Use Taylor series expansions to…

Algebra & Trigonometry with Analytic Geometry

13th Edition

ISBN:9781133382119

Author:Swokowski

Publisher:Swokowski

Chapter10: Sequences, Series, And Probability

Section10.5: The Binomial Theorem

Problem 37E

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Answer is given BUT need full detailed steps and process since I don't understand the concept.

3. Use Taylor series expansions to determine the error in the approxima-
tion u"(t) z u(t+3h)-3u(t+2h)+3u(t+h)-u(t)
=u+3hu'+(36)e u!l+
(34 "' (34)*
-3 u&+26) =u+2hu' +
24
u fthl =uthul
to
24
3
l a? u" +
+ 13
(6) +
4" (36)
num =
24
%3D
4 Find AR which make the approimation

Expert Solution

Step 1

The Taylor's thoerem can be used to calculate the expansion of a function. The formula for the Taylor's series is $f (x - a) = f (a) + \frac{f' (a)}{1!} {(x - a)}^{1} + \frac{f'' (a)}{2!} {(x - a)}^{2} + \frac{f''' (a)}{3!} {(x - a)}^{3} + f$ ⁴(a)4!(x-a)4+… .