Limit Continuity and Differentiability 7 Question 12

12. If f and g are differentiable functions in (0,1) satisfying f(0)=2=g(1),g(0)=0 and f(1)=6, then for some c0,1[

(2014 Main)

(a) 2f(c)=g(c)

(b) 2f(c)=3g(c)

(c) f(c)=g(c)

(d) f(c)=2g(c)

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Answer:

Correct Answer: 12. (a,b,d)

Solution:

  1. Given, y=sec(tan1x)

 Let tan1x=θx=tanθy=secθ=1+x2

On differentiating w.r.t. x, we get

dydx=121+x22x At x=1,dydx=12



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