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2. | а) Determine the value of the following limits: ax? а- I. ,2 x 1+x? 1+x II. 1+x 1+x b) Find the differential coefficient of the following functions w.r.t. x²sinsin (1-x) I. sinsin 2x a 1-coscos x 1+coscos x II. tantan c) If f(x)=In(sinx) and ø(x)=In(cosx), show that e 20(x) 2f(a) – eº(2a)

2. | а) Determine the value of the following limits: ax? а- I. ,2 x 1+x? 1+x II. 1+x 1+x b) Find the differential coefficient of the following functions w.r.t. x²sinsin (1-x) I. sinsin 2x a 1-coscos x 1+coscos x II. tantan c) If f(x)=In(sinx) and ø(x)=In(cosx), show that e 20(x) 2f(a) – eº(2a)

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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2. a) Determine the value of the following limits: a-x? а- 1. ,2 1+x? 1+x I. 1+x° 1+x b) Find the differential coefficient of the following functions w.r.t. x: x'sinsin (1-x) I. sinsin 2x a 1-coscos x 1+coscos x II. tantan c) If f(x)=In(sinx) and ø(x)=In(cosx), show that e 20(x) -e2f(a) = e°(2a)
Transcribed Image Text:2. a) Determine the value of the following limits: a-x? а- 1. ,2 1+x? 1+x I. 1+x° 1+x b) Find the differential coefficient of the following functions w.r.t. x: x'sinsin (1-x) I. sinsin 2x a 1-coscos x 1+coscos x II. tantan c) If f(x)=In(sinx) and ø(x)=In(cosx), show that e 20(x) -e2f(a) = e°(2a)
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