Combining power series Use the geometric series
to find the power series representation for the following functions (centered at 0). Give the interval of convergence of the new series.
32.
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Chapter 11 Solutions
Calculus, Single Variable: Early Transcendentals (3rd Edition)
- Use the power series 00 1 E(-1)"x". > |x| < 1 1+ x n = 0 to find a power series for the function, centered at 0. -2 1. 1 h(x) = + x? - 1 1 +X 1- x h(x) = E n = 0 Determine the interval of convergence. (Enter your answer using interval notation.)arrow_forwardFind the sum of the series It will be a function of the variable x. ∞ x8n x Σ(-1)". n=0 n!arrow_forwardhow do i solve the attached calculus question?arrow_forward
- Explain how to use the geometric series g(x) = 6 1+x function Select one: a. O b. C. replace x with replace x with replace x with 1 1-x n=0 and divide the series by 6 6 (-x) 6 = d. replace x with (-x) and divide the series by 6 e. replace x with (-x) and multiply the series by 6 x Σx". x <1 to find the series for thearrow_forwardC and Darrow_forward45-50. Binomial series a. Find the first four nonzero terms of the binomial series centered at 0 for the given function. b. Use the first four terms of the series to approximate the given quantity. 46. f(x) = √1+x; approximate √/1.06.arrow_forward
- ∞0 11. Discuss the convergence of the series 1/n², p > 0.arrow_forward1,: ? Credit Union National-Association- Using series, evaluate the inteġral I = [ f(x) dx, where f is the function whose graph is shown below. Hints: (i) The area of a triangle is (basex height). (ii) Compute the areas A1, A2, etc.., find a pattern and sum them A4 A3 A2 y=f(x) A1 0.. 1 72 2 X2 1. Apr/2021 5:00 Jain 5:00-6:10 PDT Mencses wided to Jonathaarrow_forward(-1)"n(z-4)" 3. Find the radius of convergence and interval of convergence for the power series n-1 2narrow_forward
- (Review) Determine whether the series E(-1)n+1 n3+5 Converges absolutely, converges conditionally, or diverges. n=1 a. converges absolutely b. converges conditionally c. diverges d. cannot be determined Let f(x) = 1 Which of the following are true? (2 marks) 1+2x² a) f(x) = E(-1)" 2"x²n if – 1< x < 1. n=0 b) f(x) = E(-1)" 2"x²n if – < x < %: n=0 c) T3,0(x) = 1 – 2x2 . d) f"(0) = -2³ · 3!. e) ſi H da 1+2x² E (-1)" 2"[2²n – 1). n=0arrow_forwardTrue or Flasearrow_forward(-3)-1 PL The Maclaurin series for a function f' is given by (-3) --- 71 converges to f(x) for x < R, where R is the radius of convergence of the Maclaurin series. ... and (b) Write the first four nonzero terms of the Maclaurin series for f', the derivative off. Express as a rational function for x < R.arrow_forward
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