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Compute the following limits. 1. lim nsin(2ren!). Hint: use Taylor expansion with the Lagrange Remainder at x = 0 for e'; note that sin(2mn + t) = sint for any m E Z.

Compute the following limits. 1. lim nsin(2ren!). Hint: use Taylor expansion with the Lagrange Remainder at x = 0 for e'; note that sin(2mn + t) = sint for any m E Z.

Advanced Engineering Mathematics
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
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Compute the following limits. 1. lim nsin(27en!). n00 Hint: use Taylor expansion with the Lagrange Remainder at x = 0 for e'; note that sin(2mn + t) = sint for any m E Z. 2. lim tanr-sin r r→0 sin -x cos z Hint: use Taylor expansion with the Peano Remainder up to o(x*). To derive Taylor expansion for tan x, you can use * + o(2*) 1-(플 + 0(23)) sin x = (z -+ o(x*)) Cos x p2 (1+(- 2 + o(x*) + + o(x*))² + o(x*)) 2
Transcribed Image Text:Compute the following limits. 1. lim nsin(27en!). n00 Hint: use Taylor expansion with the Lagrange Remainder at x = 0 for e'; note that sin(2mn + t) = sint for any m E Z. 2. lim tanr-sin r r→0 sin -x cos z Hint: use Taylor expansion with the Peano Remainder up to o(x*). To derive Taylor expansion for tan x, you can use * + o(2*) 1-(플 + 0(23)) sin x = (z -+ o(x*)) Cos x p2 (1+(- 2 + o(x*) + + o(x*))² + o(x*)) 2
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