Deck 9: Section 7: Infinite Series

Question 1

Find the Maclaurin polynomial of degree 3 for the function.

A)
B)
C)
D)
E)

Answer 1

Question 2

Determine the values of x for which the function can be replaced by the Taylor polynomial if the error cannot exceed 0.008. Round your answer to four decimal places.

A)
B)
C)
D)
E)

Answer 2

Question 3

Find a first-degree polynomial function P₁ whose value and slope agree with the value and slope of f at . What is P₁ called?

A) ; tangent line to at
B) ; secant line to at
C) ; tangent line to at
D) ; differential of at
E) ; tangent line to at

Answer 3

; tangent line to at

Question 4

Find the Maclaurin polynomial of degree 4 for the function.

A)
B)
C)
D)
E)

Question 5

Find the Maclaurin polynomial of degree two for the function .

A)
B)
C)
D)
E)

Question 6

Consider the function and its second-degree polynomial at Compute the value of and Round your answer to four decimal places.

A)
B)
C)
D)
E)

Question 7

Find the fourth degree Maclaurin polynomial for the function.

A)
B)
C)
D)
E)

Question 8

Find the third degree Taylor polynomial centered at for the function.

A)
B)
C)
D)
E)

Question 9

Find the third Taylor polynomial for expanded about .

A)
B)
C)
D)
E)

Question 10

The fourth Taylor polynomial for , expanded about is . Use this polynomial to approximate the value of . Round your answer to four decimal places.

A) 2.9184
B) 2.6976
C) 3.0144
D) 0.5664
E) 0.5376

Question 11

Find a first-degree polynomial function P₁ whose value and slope agree with the value and slope of f at . What is P₁ called?

A) tangent line to at
B) secant line to at
C) secant line to at
D) secant line to at
E) tangent line to at

Question 12

What is a first-degree polynomial function whose value and slope agree with the value and slope of at ?

A) is the tangent line to the curve at the point
B) is the tangent line to the curve at the point
C) is the tangent line to the curve at the point
D) is the tangent line to the curve at the point
E) is the tangent line to the curve at the point

Question 13

Determine the degree of the Maclaurin polynomial required for the error in the approximation of the function to be less than 0.001.

A)
B) 2
C) 5
D) 1
E) 3

Question 14

Find the Maclaurin polynomial of degree 5 for the function.

A)
B)
C)
D)
E)

Question 15

Find the Maclaurin polynomial of degree 4 for the function.

A)
B)
C)
D)
E)

Question 16

Find a first-degree polynomial function P₁ whose value and slope agree with the value and slope of at .

A)
B)
C)
D)
E)

Question 17

Find the fourth degree Taylor polynomial centered at for the function.

A)
B)
C)
D)
E)

Question 18

Use a graphing utility to graph and P₁, a first-degree polynomial function whose value and slope agree with the value and slope of f at .

A)
B)
C)
D)
E)