The derivative of y = (1 - x)(2 - x) ... (n - x) at x = 1 is equa

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 Multiple Choice QuestionsMultiple Choice Questions

781.

If y = sinx + sinx + sinx + ... , then dydx is equal to :

  • cosx2y - 1

  • - cosx2y - 1

  • sinx1 - 2y

  • - sinx1 - 2y


782.

Given f(0) = 0 and f(x) = 11 - e- 1x for x  0. Then only one of the following statements on f (x) is true. That is f(x), is :

  • continuous at x = 0

  • not continuous at x = 0

  • both continuous and differentiable at x = 0

  • not defined at x = 0


783.

The value of f at x = 0 so that function fx = 2x - 2- xx, x  0.  is continuous at x = 0, is :

  • 0

  • log(2)

  • 4

  • log(4)


784.

If y = ax . b2x - 1, then d2ydx2 is :

  • y2 . logab2

  • y . logab2

  • y2

  • y . logab22


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785.

The value of ddxtan-1x3 - x1 - 3x is

  • 121 + xx

  • 321 + xx

  • 21 + xx

  • 321 + xx


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786.

The derivative of y = (1 - x)(2 - x) ... (n - x) at x = 1 is equal to :

  • 0

  • (- 1)(n - 1)!

  • n! - 1

  • (- 1)n - 1(n - 1)!


B.

(- 1)(n - 1)!

  y = 1 - x2 - x ... n - xOn taking log on both sides, we getlogy = log1 - x + log2 - x + ... + logn - x1ydydx = 11 - x- 1 + 12 - x- 1 + ... + 1n - x- 1   dydx = y2 - x3 - x ... n - x- 1 + ...ydydxx = 1 = 1 . 2 ... n - 1!                = - 1n - 1!


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787.

Let f(x + y) = f(x)f(y) and f(x) = 1 + sin(3x) g(x), where g(x) is continuous, then f'(x) is : 

  • f(x)g(0)

  • 3g(0)

  • f(x)cos3x

  • 3f(x)g(0)


788.

Let f be continuous on [1, 5] and differentiable in (1, 5). If f (1) = - 3 and f'(x) 9 for all x  (1, 5), then

  • f5  33

  • f5  36

  • f5  36

  • f5  9


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789.

Let f be twice differentiable function such that f"(x) = - f(x) and f'(x) = g(x), h(x) = {f(x)}2 + {g(x)}2. If h(5) = 11, then h(10) is equal to :

  • 22

  • 11

  • 0

  • 20


790.

A differentiable function f(x) is defined for all x > 0 and satisfies f(x3) = 4x4 for all x > 0. The value of f'(8) is :

  • 163

  • 323

  • 1623

  • 3223


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