The value of 12. upto three places of decimals using the method o

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 Multiple Choice QuestionsMultiple Choice Questions

361.

sin-11 + x22x is

  • continuous but not differentiable at x = 1

  • differentiable at x = 1

  • neither continuous nor differentiable at x = 1

  • continuous everywhere


362.

If x2 + y2 = atan-1yx, a > 0, then d2ydx2 at x = 0 is

  • 0

  • 2ae- π2

  • - 2ae- π2

  • None of these


363.

Find C of Lagrange's mean value theorem for the function f(x) = 3x2 + 5x + 7 in the interval [1, 3].

  • 73

  • 2

  • 32

  • 43


364.

For f(x) = (x - 1)2/3, the mean value theorem is applicable to f(x) in the interval

  • [2, 4]

  • [0, 2]

  • [- 2, 2]

  • any finite interval


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365.

The differential coefficient of f(log(x)) with respect to x, where f(x) = log(x) is

  • xlogx

  • logxx

  • xlogx- 1

  • None of these


366.

If f(x) = x + - x, x  2λ,                 x = 2, then f is continuous at x = 2, provided λ is equal to

  • 1

  • 0

  • - 1

  • 2


367.

The derivative of sec-112x2 - 1 with respect to 1 - x2 at x = 1/2 will be

  • 1/4

  • sec-114

  • 4

  • 0


368.

If x = acos3θ, y = asin3θ, then 1 + dydx2 is equal to

  • tan2θ

  • secθ

  • sec2θ

  • secθ


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369.

ddxcot-1x is equal to

  • 11 + x2

  • - 11 + x2

  • 11 + x2

  • - 11 + x2


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370.

The value of 12. upto three places of decimals using the method of Newton-Raphson, will be

  • 3.463

  • 3.462

  • 3.467

  • None of these


A.

3.463

Let x = 12 x2 = 12 x2 - 12 = 0 fx = x2 - 12On differentiating w.r.t., x, we getf'x = 2x f3 < 0 and f(4) > 0Hence, root will lie between 3 and 4.f3 < f4 x0 = 3First iteration,x1 = x0 - fx0f'x0    = 3 - 9 - 122 × 3 = 3 + 36 = 3.5Now, second iterationx2 = 3.5 - f3.5f'3.5    = 3.5 - 3.52 - 122 × 3.5 = 3.463


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