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Let f : R rarr R be a differentiable fun...

Let `f : R rarr R` be a differentiable function at x = 0 satisfying f(0) = 0 and f'(0) = 1, then the value of `lim_(x to 0) (1)/(x) . sum_(n=1)^(oo)(-1)^(n).f((x)/(n))`, is
a. 0
b. `-log2`
c. 1
d. e

A

(a)0

B

(b)`-log 2`

C

(c)1

D

(d)e

Text Solution

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

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

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

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

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

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

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

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

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

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

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

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