Differential coefficient of secx is from Mathematics C

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 Multiple Choice QuestionsMultiple Choice Questions

251.

If function fx = x,         if x is rational1 - x, if x is irrational, then the number of points at which f(x) is continuous, is

  • 1

  • 0

  • None of these


252.

If xmyn = (x + y)m + n, then dydx is

  • x +yxy

  • xy

  • xy

  • yx


253.

Function f(x) = x - 1,   x <22x - 3, x  2 is a continuous function

  • for x = 2 only

  • for all real values of x such that x  2

  • for all real values of x

  • for all integral values of x only


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254.

Differential coefficient of secx is

  • 14xsecxsinx

  • 14xsecx32 . sinx

  • 12xsecx . sinx

  • 12xsecx32 . sinx


B.

14xsecx32 . sinx

Let y = secxOn differentiating w.r.t. x, we getdydx = 12secx- 12 . ddxsecx      = 12secx . secx . tanx . 12x      = 14xsecx12sinxcosx      = 14xsecx12 . sinxsecx      = 14xsecx32 . sinx


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255.

x = 0, the function f(x) = x is

  • continuous but not differentiable

  • discontinuous and differentiable

  • discontinuous and not differentiable

  • continuous and differentiable


256.

Let f(x) = sinπx5x, x  0k,            x = 0if f(x) is continuous at x = 0, then k is equal to

  • π5

  • 5π

  • 1

  • 0


257.

ddxtan-11 + x2 - 1x is equal to :

  • 11 + x2

  • x221 + x21 + x2 - 1

  • 21 + x2

  • 121 + x2


258.

ddxtan-11 + cosx21 - cosx2 is equal to :

  • - 1/4

  • 1/4

  • - 1/2

  • 1/2


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259.

If f(x) = xx - x +1, then :

  • f(x) is continuous but not differentiable at x = 0

  • f(x) is not differentiable at x = 0

  • f(x) is differentiable at x = 0

  • None of the above


260.

Let y = t10 + 1 and x = t8 + 1, then d2ydx2 is equal to :

  • 52t

  • 20t8

  • 516t6

  • None of these


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