# Calculus and Its Applications

Mathematics

## Quiz 11 :

Taylor Polynomials and Infinite Series

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Q01

Determine the second Taylor polynomial of sin at x = 0.
Enter an unlabeled polynomial in x in standard form (i.e., highest powers first).

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Short Answer

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Q02

Determine the third Taylor polynomial of f(x) = - 3x at x = 0.
Enter an unlabeled polynomial in x in standard form (i.e., highest powers first).

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Short Answer

- 3x

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Q03

Determine the third Taylor polynomial of f(x) = at x = 0.
Enter your answer as an unlabeled polynomial in x in standard form (i.e., highest powers first).

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Short Answer

+ + x + 1

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Q04

Let f(x) = ln(1 + x). Determine the third Taylor polynomial of f(x) at x = 0.

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Multiple Choice

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Q05

Let f(x) = . Determine the fourth Taylor polynomial at x = 0.

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Multiple Choice

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Q06

Find the second Taylor polynomial for f(x) = at x = 0 and use it to approximate .
Enter just a real number rounded off to two decimal places.

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Short Answer

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Q07

Find the second Taylor polynomial of f(x) = sin at x = 0 and use it to approximate the area under the curve f(x) between 0 and .
Enter an unlabeled polynomial in x in standard form followed by a comma and then just a quotient representing the area (π in the numerator).

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Q08

Find the third Taylor polynomial of f(x) = + sin x at x = 0.
Enter an unlabeled polynomial in x in standard form (i.e., highest powers first).

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Q09

Find the third Taylor polynomial of f(x) = at x = 0 and use it to approximate e.
Enter just a reduced fraction of form .

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Q10

Find the third Taylor polynomial of f(x) = sin x at x = 0 and use it to approximate .
Enter just a real number rounded off to two decimal places.

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Q11

Write down the fourth Taylor polynomial of f(x) = at x = 0.
Enter your answer an an unlabeled polynomial in x in standard Taylor polynomial form (i.e., constant first, highest power last ).

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Short Answer

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Q12

Suppose f(x) = - 7 + 2. The fifth Taylor polynomial of f(x) at x = 0 is .

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True False

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Q13

Suppose f(x) = - 7 + 2. The third Taylor polynomial of f(x) at x = 0 is .

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True False

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Q14

The area of a circle with radius 1 is π. If f(x) = gives the top half of this circle, as illustrated below, use the second Taylor polynomial of f(x) at x = 0 to find an approximate value for π. Is the following correct? Enter "yes" or "no".

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Q15

Is this the graph of y = and are its first two Taylor polynomials at x = 0 on the same axis? Enter "yes" or "no".

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Q16

Estimate by using the second Taylor polynomial for f(x) = . Is the solution?
Enter "yes" or "no".

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Short Answer

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Q17

Let f(x) = . Determine the second Taylor polynomial (x) of f(x) at x = 0.

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Multiple Choice

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Q18

Let f(x) = - 4x - 1. Which of the following statements is true? (All Taylor polynomials are at x = 0.)

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Multiple Choice

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Q19

The function f(x) = sin is approximated by its second Taylor polynomial (x) at x = 0. Which of the following statements is NOT true?

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Multiple Choice

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Q20

If f(x) = 2 + 3x - 2 + 2 , then what i f'''(0)?
Enter just an integer.

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Short Answer