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Consider the function f(x)={xsinpi/x ,f...

Consider the function `f(x)={xsinpi/x ,forx >0 0,forx=0` The, the number of point in (0,1) where the derivative `f^(prime)(x)` vanishes is 0 (b) 1 (c) 2 (d) infinite

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BANSAL-APPLICATION OF DERIVATIVE-All Questions
  1. f is continuous in [a, b] and differentiable in (a, b) (where a>0 ) su...

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  2. f(x) and g(x) are differentiable functions for 0 <= x <= 2 such that f...

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  3. Consider the function f(x)={xsinpi/x ,forx >0 0,forx=0 The, the numb...

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  4. The function f(x)=(log(pi+x))/(log(e+x))s is

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  5. The length of the longest interval in which the function 3sinx-4sin^3x...

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  6. Using the relation 2(1-cosx)<x^2,x!=0 or otherwise, prove that s in(t ...

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  7. Given a function f:[0,4]toR is differentiable ,then prove that for som...

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  8. If f(x)={(x^(alpha)logx , x > 0),(0, x=0):} and Rolle's theorem is ap...

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  9. If f(x) is differentiable and strictly increasing function, then the v...

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  10. Using Rolles theorem, prove that there is at least one root in (45^(1/...

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  11. Let f(x) be a twice differentiable function for all real values of x a...

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  12. let f(x)=2+cosx for all real x Statement 1: For each real t, there ex...

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  13. If a continuous function f defined on the real line R , assumes ...

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  14. (i) The positive value of k for which ke^x-x=0 has only one root is

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  15. (i) The positive value of k for which ke^x-x=0 has only one root is

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  16. If x is a negative integer, then x+|x|=0 (b) x-|x|=0 x+|x|=-2x ...

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  17. Number of critical point of the function f(X) =x+sqrt(|x|) is .

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  18. x+[x]

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  19. Let the function g:(-oo,oo)rarr (-pi //2,pi//2) be given by g(u) = 2 t...

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  20. Let f(x) be a non-constant twice differentiable function defined on (...

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