-1( t) (자2) + () (x-2)* -Which of the following Showsthefirst 3 terms of the Taglor SeriesBxpansion for about x>2?A. :1- - ... + ..(x-2) + (x-2)".B. 솟1(t) (7) + (t) (x-2)" - . +- .C. : -(x -2)+ (x-2)²-D. None of the above.

Name: -1( t) (자2) + () (x-2)* -Which of the following Showsthefirst 3 terms
Uploaded: 2024-03-20T06:38:44.000Z
Channel: Bartleby
Description: -1( t) (자2) + () (x-2)* -Which of the following Showsthefirst 3 terms of the Taglor SeriesBxpansion for about x>2?A. :1- - ... + ..(x-2) + (x-2)".B. 솟1(t) (7) + (t) (x-2)" - . +- .C. : -(x -2)+ (x-2)²-D. None of the above.

Answered: Whch of the following Showe the first 3…

Calculus: Early Transcendentals

8th Edition

ISBN:9781285741550

Author:James Stewart

Publisher:James Stewart

Chapter1: Functions And Models

Section: Chapter Questions

Problem 1RCC: (a) What is a function? What are its domain and range? (b) What is the graph of a function? (c) How...

See similar textbooks

Related questions

Concept explainers

Topic Video

Question

-1( t) (자2) + () (x-2)* -
Which of the following Shows
the
first 3 terms of the Taglor Series
Bxpansion for about x>2?
A. :1- - ... + ..
(x-2) + (x-2)".
B. 솟1(t) (7) + (t) (x-2)" - . +- .
C. : -(x -2)+ (x-2)²-
D. None of the above.

Expert Solution

Step 1

$G i v e n, f (x) = \frac{1}{x} w e h a v e t o d e t e r m i n e t h e f i r s t 3 t e r m s o f t h e t a y l o r s e r i e s e x p a n s i o n f o r g i v e n f (x) a b o u t x = 2 .$

Step 2

$W e k n o w t h a t a t a y l o r s e r i e s i s g i v e n b y f (x) = \sum_{k = 0}^{\infty} \frac{f^{(k)} (a)}{k!} {(x - a)}^{k} S o, w h a t w e n e e d t o d o t o g e t t h e d e s i r e d p o l y n o m i a l i s t o c a l c u l a t e t h e d e r i v a t i v e s, e v a l u a t e t h e m a t t h e g i v e n p o i n t, a n d p l u g t h e r e s u l t s i n t o t h e g i v e n f o r m u l a . f^{(0)} (x) = f (x) = \frac{1}{x} E v a l u a t e t h e f u n c t i o n a t t h e p o i n t f (2) = \frac{1}{2} w e h a v e t o f i n d f i r s t d e r i v a t i v e : f^{(1)} (x) = \frac{d}{d x} f (x) = \frac{d}{d x} (\frac{1}{x}) = \frac{- 1}{x^{2}} E v a l u a t e t h e 1 s t d e r i v a t i v e a t t h e g i v e n p o i n t f^{(1)} (2) = \frac{- 1}{4} w e h a v e t o f i n d s e c o n d d e r i v a t i v e : f^{(2)} (x) = \frac{d^{2}}{d x^{2}} f (x) = \frac{d^{2}}{d x^{2}} (\frac{1}{x}) = \frac{2}{x^{3}} E v a l u a t e t h e s e c o n d d e r i v a t i v e a t t h e g i v e n p o i n t f^{(2)} (2) = \frac{1}{4}$

Step by step

Solved in 3 steps

Knowledge Booster

$Propositional Calculus$

Learn more about

Need a deep-dive on the concept behind this application? Look no further. Learn more about this topic, calculus and related others by exploring similar questions and additional content below.

Similar questions