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_forwardRefer to imagearrow_forwardDefine Find the values of x where the series converges and show that we get a continuous function on this set.arrow_forward
- Use 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_forwardThe questions are multiple-choice, all of them with a set of possible answers, which are true or false.arrow_forwardFind the half range cosine (по косинусам) or sine (по синусам) series for each of two given functions.arrow_forward
- Algebra & Trigonometry with Analytic GeometryAlgebraISBN:9781133382119Author:SwokowskiPublisher:Cengage