The blank in the statement “The n th Taylor polynomial of f at a is the polynomial P n ( x ) = _ _ _ _ _ _ _ _ _ _ _ ”.

Question

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Answer 1

Question

Chapter 11, Problem 1CRQ

a.

To determine

To fill: The blank in the statement “The nth Taylor polynomial of f at a is the polynomial Pn(x)=___________”.

a.

Expert Solution

Answer to Problem 1CRQ

The nth Taylor polynomial of f at a is the polynomial Pn(x)=f(a)+f′(a)(x−a)+⋯+f(n)(a)n!(x−a)n_.

Explanation of Solution

Let f be a function and its first n derivatives are defined at a.

Then the nth Taylor polynomial of f at a is the polynomial, Pn(x)=f(a)+f′(a)(x−a)+f″(a)2!(x−a)2+⋯+f(n)(a)n!(x−a)n.

Therefore, the nth Taylor polynomial of f at a is the polynomial Pn(x)=f(a)+f′(a)(x−a)+⋯+f(n)(a)n!(x−a)n_.

b.

To determine

To fill: The blank in the statement “In terms of f and its derivatives, we have Pn(a)=,P′n(a)=,…,Pn(n)(a)=___”.

b.

Expert Solution

Answer to Problem 1CRQ

In terms of f and its derivatives, we have Pn(a)=f(a)_,P′n(a)=f′(a)_,…,Pn(n)(a)=f(n)(a)n!_.

Explanation of Solution

Let f be a function and its first n derivatives are defined at a.

Then the nth Taylor polynomial of f at a is the polynomial, Pn(x)=f(a)+f′(a)(x−a)+f″(a)2!(x−a)2+⋯+f(n)(a)n!(x−a)n.

So it coincides with f(x),f′(x),…,f(n)(x) at a, that is, Pn(a)=f(a),P′n(a)=f′(a),…,Pn(n)(a)=f(n)(a)n!.

Therefore, in terms of f and its derivatives, we have Pn(a)=f(a)_,P′n(a)=f′(a)_,…,Pn(n)(a)=f(n)(a)n!_.

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Answer 2

Question

Chapter 11, Problem 1CRQ

a.

To determine

To fill: The blank in the statement “The nth Taylor polynomial of f at a is the polynomial Pn(x)=___________”.

a.

Expert Solution

Answer to Problem 1CRQ

The nth Taylor polynomial of f at a is the polynomial Pn(x)=f(a)+f′(a)(x−a)+⋯+f(n)(a)n!(x−a)n_.

Explanation of Solution

Let f be a function and its first n derivatives are defined at a.

Then the nth Taylor polynomial of f at a is the polynomial, Pn(x)=f(a)+f′(a)(x−a)+f″(a)2!(x−a)2+⋯+f(n)(a)n!(x−a)n.

Therefore, the nth Taylor polynomial of f at a is the polynomial Pn(x)=f(a)+f′(a)(x−a)+⋯+f(n)(a)n!(x−a)n_.

b.

To determine

To fill: The blank in the statement “In terms of f and its derivatives, we have Pn(a)=,P′n(a)=,…,Pn(n)(a)=___”.

b.

Expert Solution

Answer to Problem 1CRQ

In terms of f and its derivatives, we have Pn(a)=f(a)_,P′n(a)=f′(a)_,…,Pn(n)(a)=f(n)(a)n!_.

Explanation of Solution

Let f be a function and its first n derivatives are defined at a.

Then the nth Taylor polynomial of f at a is the polynomial, Pn(x)=f(a)+f′(a)(x−a)+f″(a)2!(x−a)2+⋯+f(n)(a)n!(x−a)n.

So it coincides with f(x),f′(x),…,f(n)(x) at a, that is, Pn(a)=f(a),P′n(a)=f′(a),…,Pn(n)(a)=f(n)(a)n!.

Therefore, in terms of f and its derivatives, we have Pn(a)=f(a)_,P′n(a)=f′(a)_,…,Pn(n)(a)=f(n)(a)n!_.

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Answer 3

Question

Chapter 11, Problem 1CRQ

a.

To determine

To fill: The blank in the statement “The nth Taylor polynomial of f at a is the polynomial Pn(x)=___________”.

a.

Expert Solution

Answer to Problem 1CRQ

The nth Taylor polynomial of f at a is the polynomial Pn(x)=f(a)+f′(a)(x−a)+⋯+f(n)(a)n!(x−a)n_.

Explanation of Solution

Let f be a function and its first n derivatives are defined at a.

Then the nth Taylor polynomial of f at a is the polynomial, Pn(x)=f(a)+f′(a)(x−a)+f″(a)2!(x−a)2+⋯+f(n)(a)n!(x−a)n.

Therefore, the nth Taylor polynomial of f at a is the polynomial Pn(x)=f(a)+f′(a)(x−a)+⋯+f(n)(a)n!(x−a)n_.

b.

To determine

To fill: The blank in the statement “In terms of f and its derivatives, we have Pn(a)=,P′n(a)=,…,Pn(n)(a)=___”.

b.

Expert Solution

Answer to Problem 1CRQ

In terms of f and its derivatives, we have Pn(a)=f(a)_,P′n(a)=f′(a)_,…,Pn(n)(a)=f(n)(a)n!_.

Explanation of Solution

Let f be a function and its first n derivatives are defined at a.

Then the nth Taylor polynomial of f at a is the polynomial, Pn(x)=f(a)+f′(a)(x−a)+f″(a)2!(x−a)2+⋯+f(n)(a)n!(x−a)n.

So it coincides with f(x),f′(x),…,f(n)(x) at a, that is, Pn(a)=f(a),P′n(a)=f′(a),…,Pn(n)(a)=f(n)(a)n!.

Therefore, in terms of f and its derivatives, we have Pn(a)=f(a)_,P′n(a)=f′(a)_,…,Pn(n)(a)=f(n)(a)n!_.

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Answer 4

Question

Chapter 11, Problem 1CRQ

a.

To determine

To fill: The blank in the statement “The nth Taylor polynomial of f at a is the polynomial Pn(x)=___________”.

a.

Expert Solution

Answer to Problem 1CRQ

The nth Taylor polynomial of f at a is the polynomial Pn(x)=f(a)+f′(a)(x−a)+⋯+f(n)(a)n!(x−a)n_.

Explanation of Solution

Let f be a function and its first n derivatives are defined at a.

Then the nth Taylor polynomial of f at a is the polynomial, Pn(x)=f(a)+f′(a)(x−a)+f″(a)2!(x−a)2+⋯+f(n)(a)n!(x−a)n.

Therefore, the nth Taylor polynomial of f at a is the polynomial Pn(x)=f(a)+f′(a)(x−a)+⋯+f(n)(a)n!(x−a)n_.

b.

To determine

To fill: The blank in the statement “In terms of f and its derivatives, we have Pn(a)=,P′n(a)=,…,Pn(n)(a)=___”.

b.

Expert Solution

Answer to Problem 1CRQ

In terms of f and its derivatives, we have Pn(a)=f(a)_,P′n(a)=f′(a)_,…,Pn(n)(a)=f(n)(a)n!_.

Explanation of Solution

Let f be a function and its first n derivatives are defined at a.

Then the nth Taylor polynomial of f at a is the polynomial, Pn(x)=f(a)+f′(a)(x−a)+f″(a)2!(x−a)2+⋯+f(n)(a)n!(x−a)n.

So it coincides with f(x),f′(x),…,f(n)(x) at a, that is, Pn(a)=f(a),P′n(a)=f′(a),…,Pn(n)(a)=f(n)(a)n!.

Therefore, in terms of f and its derivatives, we have Pn(a)=f(a)_,P′n(a)=f′(a)_,…,Pn(n)(a)=f(n)(a)n!_.

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Answer 5

Chapter 11, Problem 1CRQ

a.

To determine

To fill: The blank in the statement “The nth Taylor polynomial of f at a is the polynomial Pn(x)=___________”.

a.

Expert Solution

Answer to Problem 1CRQ

The nth Taylor polynomial of f at a is the polynomial Pn(x)=f(a)+f′(a)(x−a)+⋯+f(n)(a)n!(x−a)n_.

Explanation of Solution

Let f be a function and its first n derivatives are defined at a.

Then the nth Taylor polynomial of f at a is the polynomial, Pn(x)=f(a)+f′(a)(x−a)+f″(a)2!(x−a)2+⋯+f(n)(a)n!(x−a)n.

Therefore, the nth Taylor polynomial of f at a is the polynomial Pn(x)=f(a)+f′(a)(x−a)+⋯+f(n)(a)n!(x−a)n_.

b.

To determine

To fill: The blank in the statement “In terms of f and its derivatives, we have Pn(a)=,P′n(a)=,…,Pn(n)(a)=___”.

b.

Expert Solution

Answer to Problem 1CRQ

In terms of f and its derivatives, we have Pn(a)=f(a)_,P′n(a)=f′(a)_,…,Pn(n)(a)=f(n)(a)n!_.

Explanation of Solution

Let f be a function and its first n derivatives are defined at a.

Then the nth Taylor polynomial of f at a is the polynomial, Pn(x)=f(a)+f′(a)(x−a)+f″(a)2!(x−a)2+⋯+f(n)(a)n!(x−a)n.

So it coincides with f(x),f′(x),…,f(n)(x) at a, that is, Pn(a)=f(a),P′n(a)=f′(a),…,Pn(n)(a)=f(n)(a)n!.

Therefore, in terms of f and its derivatives, we have Pn(a)=f(a)_,P′n(a)=f′(a)_,…,Pn(n)(a)=f(n)(a)n!_.

Answer 6

Chapter 11, Problem 1CRQ

a.

To determine

To fill: The blank in the statement “The nth Taylor polynomial of f at a is the polynomial Pn(x)=___________”.

a.

Expert Solution

Answer to Problem 1CRQ

The nth Taylor polynomial of f at a is the polynomial Pn(x)=f(a)+f′(a)(x−a)+⋯+f(n)(a)n!(x−a)n_.

Explanation of Solution

Let f be a function and its first n derivatives are defined at a.

Then the nth Taylor polynomial of f at a is the polynomial, Pn(x)=f(a)+f′(a)(x−a)+f″(a)2!(x−a)2+⋯+f(n)(a)n!(x−a)n.

Therefore, the nth Taylor polynomial of f at a is the polynomial Pn(x)=f(a)+f′(a)(x−a)+⋯+f(n)(a)n!(x−a)n_.

Answer 7

Chapter 11, Problem 1CRQ

a.

To determine

To fill: The blank in the statement “The nth Taylor polynomial of f at a is the polynomial Pn(x)=___________”.

Answer 8

a.

Expert Solution

Answer to Problem 1CRQ

The nth Taylor polynomial of f at a is the polynomial Pn(x)=f(a)+f′(a)(x−a)+⋯+f(n)(a)n!(x−a)n_.

Answer 9

a.

Expert Solution

Answer 10

a.

Expert Solution

Answer 11

Expert Solution

Answer 12

Explanation of Solution

Let f be a function and its first n derivatives are defined at a.

Then the nth Taylor polynomial of f at a is the polynomial, Pn(x)=f(a)+f′(a)(x−a)+f″(a)2!(x−a)2+⋯+f(n)(a)n!(x−a)n.

Therefore, the nth Taylor polynomial of f at a is the polynomial Pn(x)=f(a)+f′(a)(x−a)+⋯+f(n)(a)n!(x−a)n_.

Answer 13

b.

To determine

To fill: The blank in the statement “In terms of f and its derivatives, we have Pn(a)=,P′n(a)=,…,Pn(n)(a)=___”.

b.

Expert Solution

Answer to Problem 1CRQ

In terms of f and its derivatives, we have Pn(a)=f(a)_,P′n(a)=f′(a)_,…,Pn(n)(a)=f(n)(a)n!_.

Explanation of Solution

Let f be a function and its first n derivatives are defined at a.

Then the nth Taylor polynomial of f at a is the polynomial, Pn(x)=f(a)+f′(a)(x−a)+f″(a)2!(x−a)2+⋯+f(n)(a)n!(x−a)n.

So it coincides with f(x),f′(x),…,f(n)(x) at a, that is, Pn(a)=f(a),P′n(a)=f′(a),…,Pn(n)(a)=f(n)(a)n!.

Therefore, in terms of f and its derivatives, we have Pn(a)=f(a)_,P′n(a)=f′(a)_,…,Pn(n)(a)=f(n)(a)n!_.

Answer 14

b.

To determine

To fill: The blank in the statement “In terms of f and its derivatives, we have Pn(a)=,P′n(a)=,…,Pn(n)(a)=___”.

Answer 15

b.

Expert Solution

Answer to Problem 1CRQ

In terms of f and its derivatives, we have Pn(a)=f(a)_,P′n(a)=f′(a)_,…,Pn(n)(a)=f(n)(a)n!_.

Answer 16

b.

Expert Solution

Answer 17

b.

Expert Solution

Answer 18

Expert Solution

Answer 19

Explanation of Solution

Let f be a function and its first n derivatives are defined at a.

Then the nth Taylor polynomial of f at a is the polynomial, Pn(x)=f(a)+f′(a)(x−a)+f″(a)2!(x−a)2+⋯+f(n)(a)n!(x−a)n.

So it coincides with f(x),f′(x),…,f(n)(x) at a, that is, Pn(a)=f(a),P′n(a)=f′(a),…,Pn(n)(a)=f(n)(a)n!.

Therefore, in terms of f and its derivatives, we have Pn(a)=f(a)_,P′n(a)=f′(a)_,…,Pn(n)(a)=f(n)(a)n!_.

Answer 20

Ch. 11.1 - Prob. 1CQ Ch. 11.1 - Prob. 2CQ Ch. 11.1 - Prob. 1E Ch. 11.1 - In Exercises 110, find the first three Taylor...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 blank in the statement “The n th Taylor polynomial of f at a is the polynomial P n ( x ) = _ _ _ _ _ _ _ _ _ _ _ ”.

Videos

To fill: The blank in the statement “The nth Taylor polynomial of f at a is the polynomial Pn(x)=___________”.

Answer to Problem 1CRQ

Explanation of Solution

To fill: The blank in the statement “In terms of f and its derivatives, we have Pn(a)=,P′n(a)=,…,Pn(n)(a)=___”.

Answer to Problem 1CRQ

Explanation of Solution

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Chapter 11 Solutions

The blank in the statement “The n th Taylor polynomial of f at a is the polynomial P n ( x ) = _ _ _ _ _ _ _ _ _ _ _ ”.

Videos

To fill: The blank in the statement “The nth Taylor polynomial of f at a is the polynomial Pn(x)=___________”.

Answer to Problem 1CRQ

Explanation of Solution

To fill: The blank in the statement “In terms of f and its derivatives, we have Pn(a)=______,P′n(a)=______,…,Pn(n)(a)=_______”.

Answer to Problem 1CRQ

Explanation of Solution

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Chapter 11 Solutions

To fill: The blank in the statement “In terms of f and its derivatives, we have Pn(a)=,P′n(a)=,…,Pn(n)(a)=___”.