Taylor Polynomial

Taylor Polynomial

12th Grade

14 Qs

quiz-placeholder

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Taylor Polynomial

Taylor Polynomial

Assessment

Quiz

Mathematics

12th Grade

Practice Problem

Hard

CCSS
HSF.LE.A.2

Standards-aligned

Created by

Anthony Clark

FREE Resource

14 questions

Show all answers

1.

MULTIPLE CHOICE QUESTION

1 min • 1 pt

Media Image

The answer in third-degree Taylor polynomial for f(x)=ln x, centered at a = 2 is ln(2) + ½(x+2) – 1/8(x-2)2 + 1/24(x-2)3.

true

false

2.

MULTIPLE CHOICE QUESTION

1 min • 1 pt

Media Image

What is the second derivative for finding the nth Taylor polynomial of y= In x at x=1?

-2

2

-1

1

3.

MULTIPLE CHOICE QUESTION

1 min • 1 pt

Media Image

Which of the following gives the Taylor polynomial of order three of the function f(x) = sin x at a = π/2?

a.) 1- (x- π/2) ²/ 2!

b.) –(x-π/2) + (x-π/2) ³/3!

c.) (x-π/2) -(x-π/2) ³

d.) (x+π/2) + (x-π/2) ²

4.

MULTIPLE CHOICE QUESTION

1 min • 1 pt

Media Image

17. Write out the general formula for the fourth degree Taylor Polynomial of a function f (x) at a. The following is the fourth-order Taylor Polynomial of a function f(x) at a =3. What is f(²) (3)?

a.) 5

b.) 6π

c.) 20

d.) 3

Tags

CCSS.HSF.LE.A.2

5.

MULTIPLE CHOICE QUESTION

1 min • 1 pt

Media Image

The following is the fifth order Taylor Polynomial of the function f(x) at a T5(x) = 2-2(x-a) +√5(x-a) ²-π/2(x-a) ³+(x-a) ⁴+13(x-a) ⁵. What is f(³)(a)?

a.) 2√5

b.) -3π

c.) -π/2

d.) √5

Tags

CCSS.HSF.LE.A.2

6.

MULTIPLE CHOICE QUESTION

1 min • 1 pt

Media Image

Which of the following is the third Taylor Polynomial of the function f(x) = sin (x/2) centered at a = π?

(x-π) – (x-π) ³/3!

1- (x-π/2) ²/4(2!)

1- x²/4(2!)

1- (x-π) ²/4(2!)

7.

MULTIPLE CHOICE QUESTION

1 min • 1 pt

Media Image

The following is the fourth order Taylor Polynomial of the function f(x) at a. T4(x) = 10+5(x-a) + √3(x a) ² + 1/2π(x-a) ³ + 17e(x-a) ⁴. What is f’’’(a)?

a.) 3/π

b.) 2√3

c.) 17e

d.) 1/2π

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