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For x in R, f(x) =|log(e) 2-sinx| and...

For `x in R, f(x) =|log_(e) 2-sinx| and g(x) = f(f(x)) ,` then

A

g is not differentiable at x = 0

B

g'(0) = cos (log 2)

C

g'(0) = - cos (log 2)

D

g is differentiable at x = 0 and g'(0) = - sin(log 2)

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The correct Answer is:
B
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ARIHANT MATHS-CONTINUITY AND DIFFERENTIABILITY-Exercise (Questions Asked In Previous 13 Years Exam)
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  2. Let f: R to R and g:R to R be respectively given by f(x) =|x|+1 and g...

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  3. Let f(x)={x^2|(cos)pi/x|, x!=0 and 0,x=0,x in RR, then f is a. differ...

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  4. Q. For every integer n, leta(n) and b(n) be real numbers. Let functio...

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  5. Let f:R->R be a function such that f(x+y)=f(x)+f(y),AA x, y in R. a. ...

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  6. If f(x) ={{:(-x=(pi)/(2),xle -(pi)/(2)), (- cos x, -(pi)/(2)lt x ,le ...

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  7. For the function f(x)=x cos ""1/x, x ge 1 which one of the following i...

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  8. If lim(xtooo)((x^(2)+x+1)/(x+1)-ax-b)=4, then

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  10. If f(x)=x-[x], where [x] is the greatest integer less than or equal to...

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  11. Check the differentiability if f(x) = min. {1, x^(2), x^(3)}.

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  12. Fill in the blank, in the statement given below. Let f(x) = x|x The ...

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  13. lf is a differentiable function satisfying f(1/n)=0,AA n>=1,n in I, th...

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  14. The domain of the derivative of the function f(x)={{:(tan^(-1)x ,if|x|...

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  15. The left hand derivative of f(x) = [x] sin (pi x)"at x" = k is an inte...

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  16. Which of the following functions is differentiable at x = 0 ?

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  17. For x in R, f(x) =|log(e) 2-sinx| and g(x) = f(f(x)) , then

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  18. If the function g(X) ={{:( ksqrt ( x+1), 0 le x le 3),( mx+2, 3 lt x...

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  19. If f and g are differentiable functions in [0, 1] satisfying f(0)""=""...

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  20. The function f(x) = [x] cos((2x-1)/2) pi where [ ] denotes the greate...

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