If f : R → R is defined&n

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 Multiple Choice QuestionsMultiple Choice Questions

411.

If xy = yx, then xx - ylogxdydx is equal to :

  • yy - xlogy

  • yy + xlogy

  • xx + ylogx

  • xy - xlogy


412.

fx = exsinx, then f6x = ?

  • e6xsin6x

  • - 8excosx

  • 8exsinx

  • 8excosx


413.

If f(x) = 1 - 2sinxπ - 4x if x  π4            a            if x = π4is continuous at π4, then a is equal to :

  • 4

  • 2

  • 1

  • 14


414.

If u = sin-1x2 + y2x + y then xux + yuy is

  • sin(u)

  • tan(u)

  • cos(u)

  • cot(u)


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415.

If f(x, y) = cosx - 4ycosx + 4y, then fxy = x2 is equal to

  • - 1

  • 0

  • 1

  • 2


416.

y = log1 +x1 - x14 - 12tan-1x, then dydx is equal to

  • x1 - x2

  • x21 - x4

  • x1 +x4

  • x1 - x4


417.

x = cosθ, y = sin5θ  1 - x2d2ydx2 - xdydx is equal to

  • - 5y

  • 5y

  • 25y

  • - 25y


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418.

If f : R  R is defined by fx = cos3x - cosxx2, for x  0                   λ,        for x = 0and if f is continuous at x = 0, then λ = ?

  • - 2

  • - 4

  • - 6

  • - 8


B.

- 4

Given that,fx = cos3x - cosxx2, for x  0                   λ,        for x = 0Now, LHL = limx0 -fx                =limx0 - cos3x - cosxx2                = limh0cos0 - h - cos0 - h0 - h2                = limh0cos3h - coshh2                = limh0 - 3hsin3h + sinh2h Using L' Hospital rule                = - 9 + 12 = - 4Since, f(x) is continuous at x = 0 limx0 -fx = f(0) - 4 = λ  λ = - 4


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419.

If f(2) = 4 and f'(2) = 1, thenlimx2xf2 - 2fxx - 2 = ?

  • - 2

  • 1

  • 2

  • 3


420.

If y = sinlogex, then x2d2ydx2 + xdydx is equal to

  • y = sinlogex

  • coslogex

  • y2

  • - y


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