If y = x2x + 32x + 1, the

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 Multiple Choice QuestionsMultiple Choice Questions

341.

The value of m for which the function f(x) = mx2, x  12x,    x > 1 is differentiable at x = 1, is

  • 0

  • 1

  • 2

  • does not exist


342.

If f(x) = b + ax,     x < 0bx - 12, x  0, is differentiable at x = 0, then (a, b) will be

  • (- 3, - 1)

  • (- 3, 1)

  • (3, 1)

  • (2, - 1)


343.

ddxtan-11 + x2 + 1 - x21 + x2 - 1 - x2 is equal to

  • - x1 - x4

  • x1 - x4

  • - 121 - x4

  • 121 - x4


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344.

If y = x2x + 32x + 1, then dydx is equal to

  • y12x + 42x + 3 - 12x + 1

  • y13x + 42x + 3 - 12x + 1

  • y13x + 42x + 3 - 1x + 1

  • None of the above


A.

y12x + 42x + 3 - 12x + 1

Given, y = x2x + 32x + 1Taking log on both sides, we get  logy = 12logx + 2log2x + 3 - 12logx +1On differentiating w.r.t. x, we get  1ydydx = dydx + 2 . 12x + 3 . 2 - 12 . 1x + 1 dydx = y12x + 42x + 3 - 12x + 1


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345.

If y = xy, then x1 - ylogxdydx is equal to

  • x2

  • y2

  • xy2

  • xy


346.

Rolle's theorem is not applicable for the function f(x) = x, where x [- 1, 1] because

  • the function f(x) is not continuous in the interval [- 1, 1]

  • the function f(x) is not differentiable in the interval (- 1, 1)

  • f- 1  f1

  • f- 1 = f1  0


347.

If the function f(x) = x3 - 6ax2 + 5x satisfies the conditions of Lagrange's Mean Value theorem for the interval [1, 2] and the tangent to the curve y = f(x) at x = 7/4 is parallel to the chord that join the points ofintersection of the curve with the ordinates x = 1 and x = 2 . Then, the value of a is

  • 3516

  • 3548

  • 716

  • 516


348.

If 2a + 3b + 6c = 0, then atleast one root of the equation ax2 + bx + c = 0, lies in the interval

  • (0, 1)

  • (1, 2)

  • (2, 3)

  • None of these


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349.

If equation y + y33 + y55 + ... = 2x + x33 + x55 + ... , then value of y is

  • x1 - x2

  • 2x1 - x2

  • 1 - x22x

  • None of these


350.

The value of 'c' of Rolle's theorem for f(x) = ex sin(x) in [0, x] is given by

  • π4

  • 3π4

  • 5π6

  • π2


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