If f(x) = sin-12x1 + x2, then f(x) is differentiab

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 Multiple Choice QuestionsMultiple Choice Questions

191.

23ex is equal to

  • 3ex

  • 3(h - 1)ex

  • 3(eh - 1)2ex

  • None of the above


192.

The value of 2Ex2 at the interval h = 1 is

  • 0

  • 1

  • 2

  • 4


193.

The value of f at x = 0 so that function fx = 2x - 2- xx0, x  0 is continuous at x = 0, is

  • 0

  • log(2)

  • 4

  • log(4)


194.

If y = ax . b2x - 1, then d2ydx2 is

  • y2logab2

  • y . logab22

  • y2

  • y . loga2b2


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195.

If f(x) = sin-12x1 + x2, then f(x) is differentiable on

  • [- 1, 1]

  • R - {- 1, 1}

  • R - (- 1, 1)

  • None of these


B.

R - {- 1, 1}

Given, f(x)= sin-12x1 + x2On differentiating w.r.t. x, we getf'x = 11 - 2x1 +x22 × ddx2x1 + x2       = 1 +x21 - x22 × 21 - x21 +x22       = 21 +x2 × 1 - x21 - x2       = 21 + x2,      if x < 1- 21 + x2, if x > 1 f'x does not exist for x = 1 i.e., x = ± 1

Hence, f (x) is differentiable on R - {- 1, 1}.


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196.

The function f (x) = e- x is

  • continuous everywhere but not differentiable at x = 0

  • continuous and differentiable everywhere

  • not continuous at x = 0

  • None of the above


197.

If y2 = ax2 + bx + c, where a, b, c are constants, then y3d2ydx2 is equal to

  • a constant

  • a function of x

  • a function of y

  • a function of x and y both


198.

The set of points where the function fx = x - 1ex is differentiable, is

  • R

  • R - {1}

  • R - {- 1}

  • R - {0}


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199.

If x = ϕt, y = ψt, then d2ydx2 is equal to

  • ϕ'ψ'' - ψ'ϕ''ϕ'2

  • ϕ'ψ'' - ψ'ϕ''ϕ'3

  • ϕ''ψ''

  • ψ''ϕ''


200.

If fx = xsin1x, x  0k,           x  = 0 is continuous at x = 0, then the value of k is

  • 1

  • - 1

  • 0

  • 2


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