If f(0)=0, f'(0)= 1, f"(0)=0, and f'''(0)=2, then which of the following is the third order Taylor polynomial generated by f(x) at x=0?

a) 2x^3+x

b) (1/3)x^3+(1/2)x

c) (2/3)x^3+x

d) 2x^3-x

e) (1/3)x^3+x

Please show all your work.

If f(0)=0, f'(0)= 1, f"(0)=0, and f'''(0)=2, then which of the following is the third order Taylor polynomial generated by f(x) at x=0?

a) 2x^3+x

b) (1/3)x^3+(1/2)x

c) (2/3)x^3+x

d) 2x^3-x

e) (1/3)x^3+x

Please show all your work.

Tutors, please sign in to answer this question.

New Wilmington, PA

The third order Taylor polynomial generated by f(x) at x=0 is of the form

P_{3}(x) = f(0) + f'(0) x + (1/2!) f''(0) x² + (1/3!) f'''(0) x³.

With f(0)=0, f'(0)= 1, f"(0)=0, and f'''(0)=2 this becomes

P_{3}(x) = x + (1/3!) 2 x³ = x + (1/3) x³ .

Charles P.

College and Test Prep Tutor: IB Papers, GRE, GMAT, MCAT, SAT, AP Exams

New York, NY

5.0
(491 ratings)

Tara W.

High school physics & engineering teacher, 17 yrs experience

New York, NY

5.0
(14 ratings)

Andrea R.

Ph.D. Tutor: K-9 Reading, Math, Writing, Test Prep, Special Needs

Wyckoff, NJ

5.0
(409 ratings)

- Math 9039
- Math Word Problem 4068
- Math Help For College 1339
- Math Problem 948
- Math Question 748
- Math Equations 932
- Algebra 4749
- Word Problem 4851
- Algebra 2 3242
- Mathematics 535

## Comments