3 Jan 2022
Problem 68a
Page 618
Section 8.7: Taylor and Maclaurin Series
Chapter 8: Infinite Sequences and Series
Textbook ExpertVerified Tutor
3 Jan 2022
Given information
Given: The piecewise function is 
.
To prove: the given piecewise function is not equal to the Maclaurin series.
Step-by-step explanation
Step 1.
Use the definition to find derivatives of the function. 
.
.Find 
.
.
This limit has the indeterminate form 
.
.Rewrite the fraction so the indeterminate form is 
, then use l'Hospital's Rule.
, then use l'Hospital's Rule.Rewrite the fraction because using l'Hospital's Rule on the original indeterminate form will only make the denominator larger each time.
will only make the denominator larger each time.A very small number (close to zero) divided by a very large number is close to zero.
Single Variable Calculus: Early Transcendentals
4th Edition, 2018
Stewart
ISBN: 9781337687805
Solutions
Chapter
Section
- Problem 1
- Problem 2a
- Problem 2b
- Problem 3
- Problem 4
- Problem 5
- Problem 6
- Problem 7
- Problem 8
- Problem 9
- Problem 10
- Problem 11
- Problem 12
- Problem 13
- Problem 14
- Problem 15
- Problem 16
- Problem 17
- Problem 18
- Problem 19
- Problem 20
- Problem 21
- Problem 22
- Problem 23
- Problem 24
- Problem 25
- Problem 26
- Problem 27
- Problem 28
- Problem 29
- Problem 30
- Problem 31
- Problem 32
- Problem 33
- Problem 34
- Problem 35
- Problem 36
- Problem 37
- Problem 38
- Problem 39
- Problem 40
- Problem 41a
- Problem 41b
- Problem 42a
- Problem 42b
- Problem 43
- Problem 44
- Problem 44a
- Problem 44b
- Problem 45
- Problem 46
- Problem 47
- Problem 48
- Problem 49
- Problem 50
- Problem 51
- Problem 52
- Problem 53
- Problem 54
- Problem 55
- Problem 56
- Problem 57
- Problem 58
- Problem 59
- Problem 60
- Problem 61
- Problem 62
- Problem 63
- Problem 64
- Problem 65
- Problem 66
- Problem 67
- Problem 68a
- Problem 68b
- Problem 69a
- Problem 69b
- Problem 69c
- Problem 70