If y = emsin-1x and 1 - x2dydx2&nbs

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 Multiple Choice QuestionsMultiple Choice Questions

211.

If x = 2cos(t) - cos(2t), y = 2sin(t) - sin(2t), then the value of d2ydx2t = π2

  • 3/2

  • 5/2

  • 5/3

  • - 3/2


212.

If f(x) = log1 +2ax - log1 - bxx,  x  0k,                                              x = 0 is contonuous at x = 0, then value of k is

  • b + a

  • b - 2a

  • 2a - b

  • 2a + b


213.

If fx = x - 3, then f'(3) is

  • - 1

  • 1

  • 0

  • does not exist


214.

If fx = xsin1x, x  00           , x = 0, then at x = 0 the function f(x) is

  • continuous

  • differentiable

  • continuous but not differentiable

  • None of the above


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215.

If Rolle's theorem for f(x) = exsinx - cosx is verified on π4, 5π4, then the value of c is

  • π3

  • π2

  • 3π4

  • π


216.

If the function f(x) defined by

fx = xsin1x, for x  0k,            for x  = 0

is continuous at x = 0, then k is equal to

 

  • 0

  • 1

  • - 1

  • 12


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217.

If y = emsin-1x and 1 - x2dydx2 = Ay2, then A is equal to

  • m

  • - m

  • m2

  • - m2


C.

m2

Given, y = emsin-1x      ...iOn differentiating both sides w.r. t. x, we get       dydx = emsin-1xddxm sin-1x  dydx = emsin-1xm × 11 - x2 1 - x2dydx = my        from Eq. (i)On squaring both sides, we get                        1 - x2dydx2 = m2y2But it is given  1 - x2dydx2 = Ay2                                        A = m2


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218.

For what value of k, the function defined by

f(x) = log1 + 2xsinx°x2, for x  0k                             , for x = 0

is continuous at x = 0 ?

  • 2

  • 12

  • π90

  • 90π


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219.

If log10x2 - y2x2 + y2 = 2, then dydx is equal to

  • - 99x101y

  • 99x101y

  • - 99y101x

  • 99y101x


220.

If g(x) is the inverse function of f(x) and f'x = 11 +x4, then g'(x) is

  • 1 + [g(x)]4

  • 1 - [g(x)]4

  • 1 + [f(x)]4

  • 11 + g(x)4


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