If y = x + y + x + y +&nb

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91.

If y = x + y + x + y + ... , then dydx is equal to

  • y + xy2 - 2x

  • y3 - x2y2 - 2xy - 1

  • y3 + x2y2 - x

  • None of these


D.

None of these

x + y + x + y + ...  y2 = x + y + x + y + ...  y2 = x + y + y y2 = x + 2y y2 - x2 = 2yOn differentiating both sides w.r.t. .x, we get            2y2 - x2ydydx - 1 = 2dydx 2y3 - xydydx - y2 - x = dydx          2y3 - 2xy - 1dydx = y2 - x dydx = y2 - x2y3 - 2xy - 1


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92.

If f : R  R is defined by

fx = 2sinx - sin2x2xcosx, if x 0a, if x = 0,           if x = 0

then the value of a so that f is continuous at 0 is

  • 2

  • 1

  • - 1

  • 0


93.

y = easin-1x  1 - x2yn + 2 - 2n + 1xyn + 1 is equal to

  • - n2 + a2yn

  • n2 - a2yn

  • n2 + a2yn

  • - n2 - a2yn


94.

The value of f(0) so that - ex + 2xx  may be continuous at x = 0 is

  • log12

  • 0

  • 4

  • - 1 + log2


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95.

Let [ ] denotes the greatest integer function and f(x) = [tan2(x)] Then,

  • limx0fx does not exist

  • f(x) is continuous at x = 0

  • f(x) is not differentiable at x = 0

  • f(x) = 1


96.

If (x + y)sinu = x2y2, then xux + yuy is equal to

  • 1e

  • 12e

  • 1e2

  • 4e4


97.

If x = 2at1 + t3 and y = 2at21 + t32, then dydx is

  • ax

  • a2x2

  • xa

  • x2a


98.

If f(x) = logx3logex2, then f'(x) at x = e is

  • 13e1 - loge2

  • 13e1 + loge2

  • 13e- 1 + loge2

  • - 13e1 + loge2


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99.

If f(x) = (x - 2)(x - 4)(x - 6) ... (x - 2n), then f'(2) is

  • (- 1)n2n - 1 (n - 1)!

  • (- 2)n - 1 (n - 1)!

  • (- 2)n n!

  • (- 1)n - 12n (n - 1)!


100.

If fx = 1 - cosxx, x  0k,                  x = 0  is continuous at x = 0, then the value of k is

  • 0

  • 1/2

  • 14

  • 12


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