Limits Evaluate the following limits using Taylor series.
9.
Trending nowThis is a popular solution!
Chapter 9 Solutions
Calculus: Early Transcendentals (2nd Edition)
Additional Math Textbook Solutions
University Calculus: Early Transcendentals (4th Edition)
Thomas' Calculus: Early Transcendentals (14th Edition)
Glencoe Math Accelerated, Student Edition
Precalculus (10th Edition)
University Calculus: Early Transcendentals (3rd Edition)
- Series ∞ n is a divergent series. Which of the following test(s) can be used to show its divergence. n=1 n²+1 (A). The Divergence Test (B). The Integral Test (C). The Limit Comparison Test (D). The Ratio Testarrow_forwardThe integral tests says that if an=f(n), then the series 2 an is convergent if and only n =1 if the integral J F(x)dx is convergent as long as the function f is BLANK-1, BLANK- 2, and BLANK-3 on the interval X21. BLANK-1 Add your answer BLANK-2 Add your answer BLANK-3 Add your answer .T dx= lim x-2dx= lim -Tl+1¬1= lim +1 = 1 Since the integral converges and therefore the series 2 K=1 K? also converges, and <1+1=2. K=1 K2arrow_forwardUse series to evaluate the limitsarrow_forward
- el/n + e2/n +...+ e(n–1)/n + en/n (b) Evaluate the limit lim n-00 Hint: Use the idea of Riemann sums and definite integral.arrow_forwardDetermine if the serie is divergent or convergent. It is convergent found the sum.arrow_forward[5] Use series to evaluate the limits of the following: (a) lim sin(h) (c) lim r sin () h0 (b) lim 1-cos(x)–arrow_forward
- If a series of positive terms converges, does it follow that the remainder R,, must decrease to zero as n-co? Explain. Choose the correct answer below. OA. R, must decrease to zero because lim R, lim f(x)dx for all positive functions x. n-00 71-400 00 lima, n+00 K=1 OC. R, does not decrease to zero because R, is positive for a series with positive terms. OD. R, does not decrease to zero because convergent series do not have remainders. OB. R, must decrease to zero because lim R, n-+00 -0.arrow_forwardiv. will give thumbs up if correct! convergent OR divergent series calculusarrow_forwardUse series to evaluate the limits in Exercisesarrow_forward
- Define Find the values of x where the series converges and show that we get a continuous function on this set.arrow_forwardhandwritten plsarrow_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
- College AlgebraAlgebraISBN:9781305115545Author:James Stewart, Lothar Redlin, Saleem WatsonPublisher:Cengage LearningAlgebra & Trigonometry with Analytic GeometryAlgebraISBN:9781133382119Author:SwokowskiPublisher:Cengage