Limit Continuity and Differentiability 1 Question 9

10. limx0(1cos2x)(3+cosx)xtan4x is equal to

(2013 Main)

(a) 4

(b) 3

(c) 2

(d) 12

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Answer:

Correct Answer: 10. (c)

Solution:

  1. Here, Extra close brace or missing open brace

[1 form ]

=elimx0xlog(1+b2)1x=elog(1+b2)=(1+b2)

Given, limx01+xlog(1+b2)1/x=2bsin2θ

x0(1+b2)=2bsin2θ

sin2θ=1+b22b

By AM GM, b+1b2b1b1/2

b2+12b1

From Eqs. (ii) and (iii),

sin2θ=1θ=±π2, as θ(π,π]



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