The number M , such that | f 4 ( c ) | ≤ M for all the values of c , for the function f ( x ) = cos x and the third remainder for f ( x ) at x = 0 is R 3 ( x ) = f ( 4 ) ( c ) 4 ! x 4

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Answer 1

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Chapter 11.1, Problem 27E

(a)

To determine

The number M, such that |f4(c)|≤M for all the values of c, for the function f(x)=cosx and the third remainder for f(x) at x=0 is R3(x)=f(4)(c)4!x4

To determine

To prove: The error R3(0.12) in using p3(0.12) as an approximation to f(0.12)=cos .12, does not exceed 8.64×10−6

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u, v and w are three coplanar vectors: ⚫ w has a magnitude of 10 and points along the positive x-axis ⚫ v has a magnitude of 3 and makes an angle of 58 degrees to the positive x- axis ⚫ u has a magnitude of 5 and makes an angle of 119 degrees to the positive x- axis ⚫ vector v is located in between u and w a) Draw a diagram of the three vectors placed tail-to-tail at the origin of an x-y plane. b) If possible, find w × (ū+v) Support your answer mathematically or a with a written explanation. c) If possible, find v. (ū⋅w) Support your answer mathematically or a with a written explanation. d) If possible, find u. (vxw) Support your answer mathematically or a with a written explanation. Note: in this question you can work with the vectors in geometric form or convert them to algebraic vectors.

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Answer 2

Question

Chapter 11.1, Problem 27E

(a)

To determine

The number M, such that |f4(c)|≤M for all the values of c, for the function f(x)=cosx and the third remainder for f(x) at x=0 is R3(x)=f(4)(c)4!x4

To determine

To prove: The error R3(0.12) in using p3(0.12) as an approximation to f(0.12)=cos .12, does not exceed 8.64×10−6

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Answer 3

Question

Chapter 11.1, Problem 27E

(a)

To determine

The number M, such that |f4(c)|≤M for all the values of c, for the function f(x)=cosx and the third remainder for f(x) at x=0 is R3(x)=f(4)(c)4!x4

To determine

To prove: The error R3(0.12) in using p3(0.12) as an approximation to f(0.12)=cos .12, does not exceed 8.64×10−6

Expert Solution & Answer

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Answer 4

Question

Chapter 11.1, Problem 27E

(a)

To determine

The number M, such that |f4(c)|≤M for all the values of c, for the function f(x)=cosx and the third remainder for f(x) at x=0 is R3(x)=f(4)(c)4!x4

To determine

To prove: The error R3(0.12) in using p3(0.12) as an approximation to f(0.12)=cos .12, does not exceed 8.64×10−6

Expert Solution & Answer

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Answer 5

Chapter 11.1, Problem 27E

(a)

To determine

The number M, such that |f4(c)|≤M for all the values of c, for the function f(x)=cosx and the third remainder for f(x) at x=0 is R3(x)=f(4)(c)4!x4

To determine

To prove: The error R3(0.12) in using p3(0.12) as an approximation to f(0.12)=cos .12, does not exceed 8.64×10−6

Answer 6

Chapter 11.1, Problem 27E

(a)

To determine

The number M, such that |f4(c)|≤M for all the values of c, for the function f(x)=cosx and the third remainder for f(x) at x=0 is R3(x)=f(4)(c)4!x4

Answer 7

Chapter 11.1, Problem 27E

(a)

To determine

The number M, such that |f4(c)|≤M for all the values of c, for the function f(x)=cosx and the third remainder for f(x) at x=0 is R3(x)=f(4)(c)4!x4

Answer 8

To determine

To prove: The error R3(0.12) in using p3(0.12) as an approximation to f(0.12)=cos .12, does not exceed 8.64×10−6

Answer 9

To determine

To prove: The error R3(0.12) in using p3(0.12) as an approximation to f(0.12)=cos .12, does not exceed 8.64×10−6

Answer 10

Expert Solution & Answer

Answer 11

Expert Solution & Answer

Answer 12

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Answer 13

Ch. 11.1 - Determine the third Taylor polynomial of f(x)=cosx...Ch. 11.1 - Prob. 2CYU Ch. 11.1 - Prob. 1E Ch. 11.1 - Prob. 2E Ch. 11.1 - Prob. 3E Ch. 11.1 - Prob. 4E Ch. 11.1 - Prob. 5E Ch. 11.1 - Prob. 6E Ch. 11.1 - Prob. 7E Ch. 11.1 - Prob. 8E

The number M , such that | f 4 ( c ) | ≤ M for all the values of c , for the function f ( x ) = cos x and the third remainder for f ( x ) at x = 0 is R 3 ( x ) = f ( 4 ) ( c ) 4 ! x 4

Solution Summary: The author analyzes the function f(x)=mathrmcosx by differentiating it from the third remainder.

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The number M, such that |f4(c)|≤M for all the values of c, for the function f(x)=cosx and the third remainder for f(x) at x=0 is R3(x)=f(4)(c)4!x4

To prove: The error R3(0.12) in using p3(0.12) as an approximation to f(0.12)=cos .12, does not exceed 8.64×10−6

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