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Limits Evaluate the following limits using Taylor series.
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Calculus: Early Transcendentals (3rd Edition)
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- Compute the following limit of the Reimann sum by completing the steps Check the answer is at the bottomarrow_forward(n²) diverges. Recall from the Laws of Exponents that 2 (n) Show that > n! (2")". n= 1 2 (n?) :? n! Which limit below is the correct limit for the Ratio Test, where an %3D 2 (n?) 2 (n2) •n! n! O A. lim В. lim 2(n + 1)2 (n+ 12) • (n + 1)! (n)! (n + 1)2 2 (n?) lim (n + 1)! C. lim D. 2 (n?) (n+ 12) n-0 2 n!arrow_forwardQ4. Find the Fourier cosine series for the function: f(x)= 1 0 1 0arrow_forward.(x -)". IT IT as Cn Write the Taylor series for f(x) = sin(x) at x = 2 2 n=0arrow_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_forwardFind the limit (if it exists). |x+7- 3 lim x→2 x- 2 а. 6 b. 1 с. 0 1 d. 6. e. Limit does not existarrow_forwardUse the ratio test to determine whether an+1 lim n→∞ an n=16 (a) Find the ratio of successive terms. Write your answer as a fully simplified fraction. For n ≥ 16, = lim n→∞ lim n→∞ 7 (6n)² converges or diverges. (b) Evaluate the limit in the previous part. Enter co as infinity and -∞o as -infinity. If the limit does not exist, enter DNE. an+1 an (c) By the ratio test, does the series converge, diverge, or is the test inconclusive? Choosearrow_forwardTaylor polynomial for f(x)=In x to approximate f(1.15) with x0=1, and n=5arrow_forwardExapnd the function using Maclurin series expansion.arrow_forwardIf 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_forward2. Let x₁>1 and Xn+1 = 2 - 1/xn for n E N. show that (xn) is bounded and monotone. Find the limit. 3 Let x. >2 and r. for n N Show that (x..) is decreasing and boundedarrow_forwardLet f(x) = (x + 2)-and Xo = 0 then the value If (0.5) – P2(0.5)| using second degree Taylor polynomials is (Use 4-digit rounding] O a. 0.0061 O b. .0016 O c.0062 O d. None of thesearrow_forwardarrow_back_iosSEE MORE QUESTIONSarrow_forward_ios
- College AlgebraAlgebraISBN:9781305115545Author:James Stewart, Lothar Redlin, Saleem WatsonPublisher:Cengage LearningAlgebra & Trigonometry with Analytic GeometryAlgebraISBN:9781133382119Author:SwokowskiPublisher:Cengage
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