The set of points where the functton f(x) = xx is differentiable

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 Multiple Choice QuestionsMultiple Choice Questions

241.

If f(x) = x - 2 and g(x) = f(f(x)), then dgxdx for x > 10 is

  • 1 or - 1

  • 1

  • - 1

  • None of these


242.

If y = sin-11 + x + 1 - x2, then the value of dydx at x = 0 is

  • 1/2

  • - 1/2

  • 0

  • None of these


243.

The distance (in metre) travelled by a vehicle in time t (in seconds) is given by the equation s = 3t3 + 2t2 + t + 1. The difference in the acceleration between t = 2 and t = 4 is

  • 36 m/s2

  • 38 m/s2

  • 45 m/s2

  • 46 m/s2


244.

If y2 = P(x) be a cubic polynomial, then 2ddxy3d2ydx2 is equal to

  • P'''(x) + P'(x)

  • P''(x)P'''(x)

  • P(x)P'''(x)

  • constant


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245.

The set of points where the functton f(x) = xx is differentiable is

  • - , 

  • - , 0  0, 

  • 0, 

  • 0, 


A.

- , 

Wev have, fx = x2,      x  0- x2,  x < 0

Clearly, f(x)is differentiable for all x > 0 and for all x < 0. So, we check the differentiability at x = 0

Now, RHD at x = 0     = ddxx2x = 0 = 2xx = 0 = 0  LHD at x = a     = ddx- x2x = 0 = - 2xx = 0 = 0 LHD at x = 0 =  RHD at x = 0

So, f(x) is differentiable for all x i.e., the set of all points where f(x) is differentiable is - ,  i.e., R.


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246.

If fx = 1 - sinxπ - 2x2 . logsinxlog1 + π2 - 4πx + 4x2, x  π2k                                                               , x = π2 is continuous at x = π2, then k is equal to

  • - 116

  • - 132

  • - 164

  • - 128


247.

The greatest value of f(x) = (x + 1)1/3 - (x - 1)1/3 on [0, 1] is

  • 1

  • 2

  • 3

  • 13


248.

If f(x) = xsin1x, x  0k           , x = 0 is continuous at x = 0, then the value of k will be

  • 1

  • - 1

  • 0

  • None of these


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249.

If f(x) = xpcos1x, x  00             , x = 0 is differentiable at x = 0, then

  • p < 0

  • 0 < p < 1

  • p = 1

  • p > 1


250.

Let f(x) = 51x, x < 0λx, x  0 and λ  R, then at x = 0

  • f is discontinuous

  • f is continuous only, if λ = 0

  • f is continuous only, whatever λ maybe

  • None of the above


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