1. This exercise will guide you through the computation of the following limit et - 1-x lim 0 3x-3 ln(1+x)* 1- x (a) Use Taylor series to compute lim x2 3x – 3 In(1+ ) (b) Use Taylor series to compute lim Then, use your computation to find lim x2 ++ 3x - 3 In(1+x) 1 (Hint: If lim f (x) = L, for some number L, what is lim f(x) =.. (c) Appropriately use your work from parts (a) and (b) above to compute e - 1- x lim a0 3x -3 ln(1+ x)

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...
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1.
This exercise will guide you through the computation of the following limit
et – 1- x
lim
x→0 3x – 3 1n(1+x)'
-
1
(a) Use Taylor series to compute lim
x2
3x – 3 In(1+ x)
x2
(b) Use Taylor series to compute lim
Then, use your computation to find lim
x2
30+ 3х — 3In(1 + x)
1
(Hint: If lim f (x) = L, for some number L, what is lim
f (x)
..)
x→a
(c) Appropriately use your work from parts (a) and (b) above to compute
et – 1 – x
lim
x→0 3x – 3 In(1+ x)
Transcribed Image Text:1. This exercise will guide you through the computation of the following limit et – 1- x lim x→0 3x – 3 1n(1+x)' - 1 (a) Use Taylor series to compute lim x2 3x – 3 In(1+ x) x2 (b) Use Taylor series to compute lim Then, use your computation to find lim x2 30+ 3х — 3In(1 + x) 1 (Hint: If lim f (x) = L, for some number L, what is lim f (x) ..) x→a (c) Appropriately use your work from parts (a) and (b) above to compute et – 1 – x lim x→0 3x – 3 In(1+ x)
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