If f(x) and g(x) are two functions with g(x) = x - 1xan

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 Multiple Choice QuestionsMultiple Choice Questions

271.

If f(x) = sin5xx2 + 2x, x  0k + 12,    x = 0 is continuous at x = 0, then the value of k is

  • 1

  • - 2

  • 2

  • 1/2


272.

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

  • x21 - x4

  • x21 + x4

  • x1 + x4

  • x1 - x4


273.

Which one of the following is not true always?

  • If f(x) is not continuous at x = a, then it is not differentiable at x = a

  • If f(x) is continuous at x = a, then it is differentiable at x = a

  • If f(x) and g(x) are differentiable at x = a, then f(x) + g(x) is also differentiable at x = a

  • If a function f(x) is continuous at x = a, then limxafx f(x) exists


274.

If y = 1 + 1x + 1x2 + 1x3 + ...  with x > 1, then dydx :

  • x2y2

  • x2y2

  • y2x2

  • - y2x2


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275.

If f(x) and g(x) are two functions with g(x) = x - 1xand fog(x) = x3 - 1x3, then f' (x) is :

  • 3x2 + 3

  • x2 - 1x2

  • 1 +1x2

  • 3x2 + 3x4


A.

3x2 + 3

We have, gx = x - 1x and fog(x) = x3 - 1x3        fgx = x - 1x3 + 3x - 1xAs           (x) = x - 1x fx - 1x = x - 1x3 + 3x - 1xLet    x - 1x = t   ft = t3 +3t  fx = x3 + 3x f'x = 3x2 + 3


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276.

If sin(x + y) + cos(x + y) = log(x + y), then d2ydx2 is :

  • - yx

  • 0

  • - 1

  • 1


277.

If f(x) is a function such that f''(x) + f(x) = 0 and g(x) = [f(x)]2 + [f'(x)]2 and (3) = 3 then g(8) is equal to :

  • 5

  • 0

  • 3

  • 8


278.

If the function f(x) = 1 - cosxx2, x  0k,                  x = 0 is continuous at x = 0, then the value of k is

  • 1

  • 0

  • 12

  • - 1


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279.

If sec-11 + x1 - y = a, then dydx is

  • y - 1x + 1

  • y + 1x - 1

  • x - 1y - 1

  • x - 1y + 1


280.

If y = cos23x2 - sin23x2, then d2ydx2 is

  • - 31 - y2

  • 9y

  • - 9y

  • 31 - y2


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