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Limits Evaluate the following limits using Taylor series.
18.
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Calculus: Early Transcendentals (3rd Edition)
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- Use 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_forwardn + 5 Use the ratio test to determine whether converges or diverges. п! n=8 Find the ratio of successive terms. Write your answer as a fully simplified fraction. For n 2 8, ап+1 lim lim %3D n-00 An Evaluate the limit in the previous part. Enter o as infinity and -o as -infinity. If the limit does not exist, enter DNE. аn+1 lim An n→00 By the ratio test, does the series converge, diverge, or is the test inconclusive? Choosearrow_forward39.. Find the Taylor polynomials (centred at zero) of degrees (a) 2, (b) 4, (c) 6, (d) 8. 1 f (x)= 1+x? a. S2(x)=1-x² s,(x)= 1-x²+x* S (x) = 1-x²+x+-x S(x)= 1-x²+xt-x°+x³ b. S2(x) = 1+x² S,(x)=1+x²+x* S(x)= 1+x²+x++x Sx)= 1+x²+x*+x°+x° c. S,(x)= 1-x² S,(x)=1-x²-x S,(x) = 1-x²-x+-x° S;(x)= 1-x²-x+-x°-x° S(x) = 1+x²-x++x d. S,(x)= 1+x² S,(x) = 1+x²-x* e. S,(x)= 1-x² S,(x)=1-x²+x* S(x)= 1-x²+x++x S,(x)=1-x²+x++x°+x® * $x)= 1+x²-x*+x°-x³arrow_forward
- 2. 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_forwardOf to noijieog Isijini as bas bnoɔ2 19g jeet I to yJibolev Isitini Use the limit process to find the area of the region between the graph of the function f(x) 9. -x2 + 9 and the x-axis over the interval [0, 3]. %3D 10. A ball is thrown vertically uNward from t hoarrow_forward4n8-9n7+6n6 Evaluate the following limit or state that it diverges lim n→∞ -7n8+9n7+3n-1' 11 steps.arrow_forward
- College AlgebraAlgebraISBN:9781305115545Author:James Stewart, Lothar Redlin, Saleem WatsonPublisher:Cengage LearningAlgebra & Trigonometry with Analytic GeometryAlgebraISBN:9781133382119Author:SwokowskiPublisher:Cengage
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