Exponential function In Section 9.3, we show that the power series for the exponential function centered at 0 is
Use the methods of this section to find the power series for the following functions. Give the interval of convergence for the resulting series.
72. f(x) = x2ex
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Calculus: Early Transcendentals (2nd Edition)
- 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.arrow_forwardUse a geometric series to represent each of the following functions as a power series about x = 0. Find the interval of convergence. a. f(x)= 5 2-X b. g(x)= 7 X-3 00 www a. The power series representation for f(x) is Σx". n=0 The interval of convergence is (Simplify your answer. Type your answer in interval notation.) b. The power series representation for g(x) is Σx". n=0 The interval of convergence is (Simplify your answer. Type your answer in interval notation.)arrow_forwardQuestion 2. Find the domain of convergence of the following series: (-1)"+1 n ln² n ∞ n=2 -x".arrow_forward
- C and Darrow_forwardwith solutionarrow_forwardFrom the following statements, choose the one(s) that are true. OA. The function f(x) = can be represented by the power series (- 1)"2"x2. 1+2x O B. The function f(x) = 1 can be represented by the power series 1 2+2x 2 OC. x"+1 00 The function f(x) = In(1+ x) can be represented by the power series O D. The power series Ln = 0 n! converges only when X=0 and has a radius of convergence of R=0. OE. The function f(x) = In(1- x) can be represented by the power series * n+1 OF. The power series *n! xn converges only when x=0 and has a radius of convergence of R=0.arrow_forward
- Algebra & Trigonometry with Analytic GeometryAlgebraISBN:9781133382119Author:SwokowskiPublisher:Cengage