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DEvaluate the foll owing limits. @ lim メー→0 eř +e-X- 2 |-cos2x Dlim, x² Inx 9. メー→0

DEvaluate the foll owing limits. @ lim メー→0 eř +e-X- 2 |-cos2x Dlim, x² Inx 9. メー→0

Calculus: Early Transcendentals
Calculus: Early Transcendentals
8th Edition
ISBN:9781285741550
Author:James Stewart
Publisher:James Stewart
Chapter1: Functions And Models
Section: Chapter Questions
Problem 1RCC: (a) What is a function? What are its domain and range? (b) What is the graph of a function? (c) How...
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I’m posting this again, im getting different answer, please show all the work, no shortcuts, write clearly showing the letters, do not write in cursive, use the table below if its possible only, thank you
D Evaluate the following limits. lim exteメ-2 メー→0 |-cos2x Jim, x² Inx 9) メ→
Transcribed Image Text:D Evaluate the following limits. lim exteメ-2 メー→0 |-cos2x Jim, x² Inx 9) メ→
Table 11.5 asserts, without proof, that in several cases the Taylor series for f converges to f at the endpoints of the interval of convergence. Proving convergence at the endpoints generally requires advanced techniques. It may also be done using the following theorem: Suppose the Taylor series for f centered at 0 converges to f on the interval (-R, R). If the series converges at x = R, then it converges to lim f(x). Table 11.5 Et for Jx < 1 11 1-x x² - ... + (-1)*x* +-. (-1)*. for x| <1 .... 1+x e = 1 +x+ E for (x| < 0 +... k! (-1)*x*+1 (2k + 1)! (-1)과+1 Σ F (2k + 1)! " If the series converges at x = -R, then it for |x| < 0 sin x =x - 3! +... = converges to lim f(x). - 5! For example, this theorem would (-1)*x* (2k)! (-1)*x* FO (2k)! allow us to conclude that the series for x x* for |x| < 0 %3! In (1 + x) converges to In 2 at x = 1. cos x = 1 - (-1)*+1 x* (-1)*+!,4 for -1 <xs1 In (1 + x) = x – 2. ....- +... - 3 k 11 k -la (1 – 3) = x +* for -1 sx< 1 ..+ + (-1)* x24+1 tanx= x- for |x| s 1 -...+ 2k + 1 2k + 1 sinh x=x + 3! 5! (2k + 1)! (2k + 1)!" for x < 0 cosh x=1 + 2! +... (2k)! E for x < 0 (1 + xy = E(")r*, for la <1 and (P)- P(p – 1)(p – 2) - . · (p – k + 1) (P) k!
Transcribed Image Text:Table 11.5 asserts, without proof, that in several cases the Taylor series for f converges to f at the endpoints of the interval of convergence. Proving convergence at the endpoints generally requires advanced techniques. It may also be done using the following theorem: Suppose the Taylor series for f centered at 0 converges to f on the interval (-R, R). If the series converges at x = R, then it converges to lim f(x). Table 11.5 Et for Jx < 1 11 1-x x² - ... + (-1)*x* +-. (-1)*. for x| <1 .... 1+x e = 1 +x+ E for (x| < 0 +... k! (-1)*x*+1 (2k + 1)! (-1)과+1 Σ F (2k + 1)! " If the series converges at x = -R, then it for |x| < 0 sin x =x - 3! +... = converges to lim f(x). - 5! For example, this theorem would (-1)*x* (2k)! (-1)*x* FO (2k)! allow us to conclude that the series for x x* for |x| < 0 %3! In (1 + x) converges to In 2 at x = 1. cos x = 1 - (-1)*+1 x* (-1)*+!,4 for -1 <xs1 In (1 + x) = x – 2. ....- +... - 3 k 11 k -la (1 – 3) = x +* for -1 sx< 1 ..+ + (-1)* x24+1 tanx= x- for |x| s 1 -...+ 2k + 1 2k + 1 sinh x=x + 3! 5! (2k + 1)! (2k + 1)!" for x < 0 cosh x=1 + 2! +... (2k)! E for x < 0 (1 + xy = E(")r*, for la <1 and (P)- P(p – 1)(p – 2) - . · (p – k + 1) (P) k!
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