Problem

Find the first three nonzero terms of the Maclaur…

Problem 16 Easy Difficulty

Find the first three nonzero terms of the Maclaurin expansion of the given functions.
$$f(x)=(4+x)^{3 / 2}$$

Answer

$8+\frac{3}{1 !} x+\frac{\frac{3}{8}}{2 !} x^{2}+\frac{-\frac{3}{64}}{3 !} x^{3}$

Related Courses

Calculus 2 / BC

Basic Technical Mathematics with Calculus

Chapter 30

Expansion of Functions in Series

Section 2

Mclaurin Series

Discussion

You must be signed in to discuss.

Top Calculus 2 / BC Educators

Watch More Solved Questions in Chapter 30

Problem 1

Problem 2

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 41

Problem 42

Problem 43

Problem 44

Video Transcript

we want to find the first three non zero terms of the MacLaurin series expenditure for the flagship acrobatics is equal to four plus x rays and power of three hats. This question is testing our ability to expand the function. Using a series. In particular, we need to know the MacLaurin series states so the MacLaurin series states that F X is equal to X zero plus F prime zero, X plus F double prime 0/2. Factorial X square plus F 3 0/3 pectoral excuse and so on. Where every time is at the end of derivative zero. Development and factorial times. Actually on four plus extra three half zero is 4-3/2 or eight. That's we need to find at least 22 rivers. Was on zero terms. To finalize this question, F one is three hast route four plus X zero. This is three. F two is 3/4. Route four plus X at zero. This is 3/8. That's from F F one and F two. We have our 1st 390 terms and plug into MacLaurin series. Our solution is eight plus three X plus 3/16 X squared and so on.

Get More Help with this Textbook

Allyn J. Washington, Richard S. Evans

Basic Technical Mathematics with Calculus

View More Answers From This Book

Find Another Textbook

Problem