Problem

Finding roots with Newton's method For the given …

03:36

Problem 16 Easy Difficulty

Finding roots with Newton's method For the given function f and initial approximation $x_{0},$ use Newton's method to approximate a root of $f .$ Stop calculating approximations when two successive
approximations agree to five digits to the right of the decimal point after rounding. Show your work by making a table similar to that in Example 1.
$$f(x)=e^{x}+x-5 ; x_{0}=1.6$$

Answer

$r \approx 1.30656$

Related Courses

Calculus 1 / AB

Calculus Early Transcendentals

Chapter 4

Applications of the Derivative

Section 8

Newton's Method

Discussion

You must be signed in to discuss.

Top Calculus 1 / AB Educators

Watch More Solved Questions in Chapter 4

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

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

Video Transcript

problem number 16 toe Approximate route are off the given function F and the initial approximation. Ex New. We used the Newton's method. The formula that we use for this is X m plus one equals xn minus fo x m over half dance off. Explain in our case F of X equals e power X Class X minus five and after dash of X, it would be our X plus one. My next note equals 1.6. We should stop calculating approximations When two successive approximations agreed to five digits toe the right off the decimal points after rounding. Now drew our table a number of iterations X men F o X and F dash of x and and X n minus. And for the Mexican my over f dash X and okay, let's use a smaller form Bigness Okay, tradition number 01 can and three Our excellent equals 1.6 and four x and 1.55 303 5.95 303 1.33912 We used this value as our next episode when 1.33912 0.15 great would win. 815 68 1.30 697 These two bodies do not agree. The four will continue for the next situation. 1.30697 0.193 4.69 496 Then this battle three, 656 These two values still do not agree toe to five digits after the decimal point. Before we continue for the Mexican situation Unlawfully, we can, uh, stop right after this. The next situation on 0.30656 0.0 Zero 006 4.69 345 and 21.30656 can see now that these two values agreed toe the five digit toe five dismount five digits after the different point before we can stop calculating our approximation.

We have video lessons for 83.18% of the questions in this textbook