If y = elog1 + x + x2 +

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 Multiple Choice QuestionsMultiple Choice Questions

231.

The function y = 2sinx is continuous for any x but it is not differentiable at

  • only x = 0

  • only x = π

  • only x = π2

  • x =  k is integer


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232.

If y = elog1 + x +x2 + x3 + , where x < 1, then dydx is equal to

  • - 11 - x2

  • 11 - x2

  • 11 + x2

  • None of these


B.

11 - x2

We have, y = elog1 + x +x2 + x3 + , where x < 1    y = 1 + x +x2 + x3 + ...    y = 11 - x = 1 - x - 1        S = a1 - r     dydx = - 11 - x- 2- 1 dydx = 11 - x2


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233.

Let f (x + y) = f(x) + f(y) for all x and y. If the function f(x) is continuous at x = 0, then f(x) is continuous

  • only at x = 0

  • at x  R - 0

  • for all x

  • None of these


234.

Let fx = x2sin1x, x  00,             x = 0. Then, f(x) is continuous but not differentiable at x = 0, if

  • n  0, 1

  • n  [1, )

  • n  - , 0

  • n = 0


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235.

The function f(x) = x2a,             0  x < 1a,                  1  x < 22b2 - 4bx2, 2  x <  is continuous for 0  x < ,then the most suitable values of a and b are

  • a = 1, b = - 1

  • a = - 1, b = 1 + 2

  • a = - 1, b = 1

  • None of the above


236.

If f(x) = 1,                  x < 01 + sinx,    0  x < π2,then at x = 0 the derivative f'(x) is

  • 1

  • 0

  • infinite

  • not defined


237.

If f(x) = 1 - cos4xx2,          when x < 0         a,                   when x = 0x16 + x - 4, when x > 0 is continuous at x = 0, then the value of a will be

  • 8

  • - 8

  • 4

  • None of these


238.

If f is a real-valued differentiable function satisfying fx - fy  (x - y)2 , x, y  R and f(0) = 0, then f(1) is equal to

  • 2

  • 1

  • - 1

  • 0


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239.

Let f(x) = - 2sinx,     - π  x  - π2asinx + b,    - π2  x  π2cosx,                  π2  x  π. If f(x) is continuous on - π, π, then

  • a = 1, b = 1

  • a = - 1, b = - 1

  • a = - 1, b = 1

  • a = 1, b = - 1


240.

If f(x) = x1 + exp1x ,     x  00                     ,     x = 0, then f(x) at x = 0 is

  • continuous

  • not continuous

  • differentiable

  • not differentiable


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