Consider tan-1 x =+∞Σn=0(-1)²n+12n + 1for all x € [-1,1].a. By differentiating tan-¹ (2²), find a power series representation of f(x)€ (-1,1).c. Approximate tanb. Use the result in item a. to find the exact value of+∞n=0(−1)n+116n=2x1+xªthat is valid for all¹) using a 4th degree Maclaurin polynomial.Hint: Using the power series representation for tan given above, write x tan¹ as a power series.

Answered: Image /qna-images/answer/9c8396f7-177b-4929-bf87-7ac520c5b478.jpg

Answered: Consider tan-1 x = C. +∞ n=0 (-1)¹x²n+1…

Algebra & Trigonometry with Analytic Geometry

13th Edition

ISBN:9781133382119

Author:Swokowski

Publisher:Swokowski

Chapter5: Inverse, Exponential, And Logarithmic Functions

Section5.6: Exponential And Logarithmic Equations

Problem 64E

See similar textbooks

Similar questions

The formula for the amount A in an investmentaccount with a nominal interest rate r at any timet is given by A(t)=a(e)rt, where a is the amount ofprincipal initially deposited into an account thatcompounds continuously. Prove that the percentageof interest earned to principal at any time t can becalculated with the formula I(t)=ert1.
Find a power series representation for the function f(x) = 1- 23 O A. (-3)x"+2 O B. En-0 373n+2 O C. (-3)r3n+2 O D. (-3)r3n
Find the coefficient of x° in the power series of this function f(x) = (1-2.x)2
Let f(x) = 1 + x 1 X Find the power series representation for the function f(x) by completing the following steps: a. First, express the fraction 1¹ as a power series. = X b. Now, express the fraction as a power series. 1-x 1+x x c. The function f(x) 1-x 1-x + 1 is the sum of the two series from parts (a) and (b). Express the function f(x) as a power series. d. What is the interval of convergence and the radius of convergence for this power series?
Which if the following is a power series representation of the function f(x) = −1+x ? +∞ a. Σ(-x" - x^²+1) b. (x² + x²+¹) +∞ n=0
Obtain the 4th term of the power series of COS(x) for a value of x = 4.91.
(-1)"x2n+1 Σ for all x E [-1, 1] Given: tan -1 X = 2n +1 n=0 2x 1. Find the power series representation of f(x) [Hint: Differentiate tan-1(x²).] 1+ x4 2. Use the result in item (1) to find the exact value of >. (-1)n+1 16" n=0 3. Approximate (tan-) using a 4th degree Maclaurin polynomial.
Determine the first 6 terms of the series of Maclaurin for f(x) = 3 cos4x.
2x 1+x2 1. Find a power series representation for f(x) Use this answer to find a power series representation for g(x) = ln(1 + x²). =
find a power series for f(x)= ln((1+x)²). ln((1+x²))= Σ n=0 and infinity
Find a power series for the function Select one: a. O b. (x-1)" m = 0 6"²+1 (x-1)" 6" O d. (x-1)" 6" O c. O e. n=0 6"+1 (x-1)" Ž M=0 n=0 n=0 (-1)" (x-1)" · 6+1 1 7-x centered at 1.
Observe the function X f(x) = (1+2x)² In order to find the power series for this function, complete the following steps: 1 1-x a. Start with the series Σ. Replace x with (−2x) in this series and k=0 write the corresponding power series for = 1 1+2x b. Take derivative of the series from part (a) above and relate it to the power series for the function 1 (1+2x)²· c. Multiply both sides of the resulting series from above with x, and obtain the series for Write the first four non-zero terms of this series. X (1+2x)² d. What is the radius of convergence for this series? What is the interval of convergence?

SEE MORE QUESTIONS

Recommended textbooks for you

Algebra & Trigonometry with Analytic Geometry

Algebra

ISBN:

9781133382119

Author:

Swokowski

Publisher:

Cengage

College Algebra

Algebra

ISBN:

9781938168383

Author:

Jay Abramson

Publisher:

OpenStax

Algebra & Trigonometry with Analytic Geometry

Algebra

ISBN:

9781133382119

Author:

Swokowski

Publisher:

Cengage

College Algebra

Algebra

ISBN:

9781938168383

Author:

Jay Abramson

Publisher:

OpenStax

SEE MORE TEXTBOOKS