Let f(2) = 4 and f'(2)= 1. Then, limx→2xf2 - 

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 Multiple Choice QuestionsMultiple Choice Questions

971.

The value of limx11 - x . tanπx2 will be

  • π2

  • 2π

  • 2π

  • π


972.

Let f(x) = x2 - 4x + 3x2 + 2x - 3, x  1k                   , x = 1 If f(x) is continuous at x = 1, then the value of k will be

  • 1

  • 12

  • - 1

  • - 12


973.

Let f(x) = xn . sin1x, x  00               , x = 0 Then, f(x) is differentiable at x = 0, if

  • n  0, 1

  • n  1, 2

  • n  1, 

  • n  - , 


974.

In which interval the function fx = log105x - x24 is defined ?

  • [1, 4]

  • [0, 5)

  • (0, 1)

  • (- 1, )


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975.

limx0x . 2x - x1 - cosx equals

  • log2

  • 12log2

  • 2log2

  • None of these


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976.

Let f(2) = 4 and f'(2)= 1. Then, limx2xf2 - 2fxx - 2 is given by

  • 2

  • - 2

  • - 4

  • 3


A.

2

limx2xf2 - 2fxx - 2Using L' Hospital's rule,limx2f2 - 2f'x1 = f2 - 2f'2                              = 4 - 2 = 2


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977.

If y = logsinxtanx, then dydxπ4 is equal to

  • 4log2

  • - 4log2

  • - 4log2

  • None of these


978.

If y = logexx - 22 for x  0, 2, then y'(3) is equal to

  • 13

  • 23

  • 43

  • None of these


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979.

sin-11 + x22x is

  • continuous but not differentiable at x = 1

  • differentiable at x = 1

  • neither continuous nor differentiable at x = 1

  • continuous everywhere


980.

If x2 + y2 = atan-1yx, a > 0, then d2ydx2 at x = 0 is

  • 0

  • 2ae- π2

  • - 2ae- π2

  • None of these


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