Taylor & Maclaurin Theorem

Last Updated :
Discuss
Comments

Question 1

The coefficient of the x5 term in the Maclaurin polynomial for sin(2x) is - 

  • 0

  •  0.0083333

  • 0.26667

  • 0.016667

Question 2

What is the value of e0.25 using the first five terms of the Maclaurin series of ex -

  • 1.2840

  • 1.384

  • 0

  • 3.269

Question 3

The Taylor series expansion of the function f(x) = (1 + x)^5 around x = 0 is given by:


  • (a) 1 + 5x + 10x² + 10x³ + 5x⁴ + x⁵

  • (b) 1 + 5x + (5/2)x² + (5/6)x³ + (5/24)x⁴ + (5/120)x⁵

  • (c) 1 + 5x + 20x² + 60x³ + 120x⁴ + 120x⁵

  • (d) 1 + x + x² + x³ + x⁴ + x⁵


Question 4

Which of the following statements about the Taylor series of f(x) = e^x, centered at x = 0, are correct?


  • A. The series converges for all real x

  • B. The Taylor series is sum(x^n / n!) from n = 0 to infinity

  • C. The remainder term always tends to zero as n approaches infinity

  • D. The radius of convergence is 1

Question 5

Let T(x) be the Maclaurin series for f(x) = ln(1−x). Which of the following statements about T(x) are true?

  • The interval of convergence for T(x) is [−1, 1).

  • The series T(1) converges to a finite value

  • The radius of convergence of T(x) is R = 1.

  • The series T(−1) diverges

Question 6

The coefficient of (x − 1)3 in the Taylor series expansion of f(x) = (1 − x) ln(x) around x = 1 is ________. (Answer up to 3 decimal places)

  • 0.500

  • -0.167

  • 0.333

  • -0.250

Question 7

Using the third-degree Taylor polynomial for f(x) = ln(1 + x) centered at x = 0, the approximate value of ln(1.5) is ____. (Answer up to 3 decimal places)

  • 0.405

  • 0.417

  • 0.500

  • 0.600

There are 7 questions to complete.

Take a part in the ongoing discussion