If yk is the kth derivative of y with respect to 'x', and y = cos

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 Multiple Choice QuestionsMultiple Choice Questions

81.

The value of limx0sinx4 - x4cosx4 + x20x4e2x4 - 1 - 2x4 is equal to

  • 0

  • - 16

  • 16

  • Does not exist


82.

The equation sinx + 2sin2x + 3sin3x = 8π has atleast one root in

  • π, 3π2

  • 0, π2

  • π2, π

  • π2, 3π4


83.

If xy = ey - x, then dydx =

  • yx - 1xy + 1

  • yx + 1xy - 1

  • x + 1y - 1

  • x - 1y + 1


84.

If y = cos-1sinx + cosx2, - π4 < x < π4, then dydx =

  • - 1

  • 1

  • 0

  • None of these


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85.

limxx + ax + ba + b is equal to

  • 1

  • 1b - a

  • ea - b

  • eb


86.

limx0x . 10x - x1 - cosx is equal to

  • log10

  • 2log10

  • 3log10

  • 4log10


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87.

If yk is the kth derivative of y with respect to 'x', and y = cos(sin(x)), then y1sinx + y2cosx is equal to

  • ysin3x

  • - ysin3x

  • ycos3x

  • - ycos3x


D.

- ycos3x

Given that, y = cossinxy1 = - sinsinxcosxy2 = - cossinxcos2x + sinsinxsinxNow, y1sinx + y2cosx    = - sinsinxsinxcosx - ycos3x         + sinsinxsinxcosx y1sinx + y2cosx = - ycos3x


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88.

limx0sinxsin-1xx2 is equal to

  • 0

  • 1

  • - 1


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89.

limx  0 4x - 9xx4x + 9x is equal to

  • log23

  • log32

  • 12log23

  • 12log32


90.

 If z = secy - ax + tany + ax, 2zx2 - a22zy2 is equal to

  • 0

  • - z

  • z

  • 2x


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