If limx→aax - xaxx - aa = 

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 Multiple Choice QuestionsMultiple Choice Questions

61.

If the normal to the curve y = f(x) at (3, 4) makes an angle 3π4 with the positive x-axis, then f'(3) is equal to :

  • - 1

  • 34

  • 1

  • 34


62.

limh0x +h - xh is equal to

  • 12x

  • 1x

  • 2x

  • x


63.

limθ05θcosθ - 2sinθ3θ + tanθ is equal to

  • 3/4

  • - 3/4

  • 0

  • None of these


64.

If cos(x + y) = ysin(x), then dydx is equal to

  • - sinx +y + ycosxsinx + sinx + y

  • sinx +y + ycosxsinx + sinx + y

  • - sinx +y + ycosxsinx + sinx + y

  • None of the above


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65.

limx2+x - 2x - 2 is equal to

  • - 1

  • 1

  • 2

  • - 2


66.

y = tan-11 + x2 + 1 - x21 + x2 - 1 - x2, then dydx is equal to

  • 11 + x2

  • - 12

  • - x1 - x4

  • x1 + x21 - x4


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67.

If limxaax - xaxx - aa = - 1, then

  • a = 1

  • a = 0

  • a = e

  • a = 1e


A.

a = 1

Given, limxaax - xaxx - aa = - 1     form 00Using L' Hospital's rulelimxaaxloga - axa - 1xx1 + logx = - 1            aaloga - aaaa1 + loga = - 1                  loga - 11 + loga = - 1                           loga = 0                                  a = 1


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68.

limx5x - 5x - 5 equals

  • 2

  • 0

  • - 2

  • None of these


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69.

limxπ3sinπ3 - x2cosx - 1 is equal to

  • 12

  • 13

  • - 13

  • 23


70.

If 2x + 2y =2x + y, then the value of dydx at x = y = 1 is

  • 0

  • - 1

  • 1

  • 2


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