Let f(x) = αxsinπx2    for 

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 Multiple Choice QuestionsMultiple Choice Questions

221.

If the function f(x) = tanπ4 + x1x for x  0 is  = K for x = 0 continuous at x = 0, then K = ?

  • e

  • e- 1

  • e2

  • e- 2


222.

If x = f(t) and y = g(t) are differentiable functions of t, then d2ydx2 is

  • f't . g''t - g't . f''tf't3

  • f't . g''t - g't . f''tf't2

  • g't . f''t - f't . g''tf't3

  • g't . f''t + f't . g''tf't3


223.

If f(x) = = logsec2xcot2x for x  0= K                         for x = 0 is continuous at x = 0, then K is

  • e- 1

  • 1

  • e

  • 0


224.

If fx = x for  x 0= 0 for x > 0, then f(x) at x = 0 is

  • continuous but not differentiable

  • not continuous but differentiable

  • continuous and differentiable

  • not continuous and not differentiable


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225.

Let f(x) = - 2sinx            if x  - π2Asinx + B if - π2 < x < π2cosx                 if x  π2

For what values of A and B, the function f(x) is continuous throughout the real line ?

  • A = - 1, B = 1

  • A = - 1, B = - 1

  • A = 1, B = - 1

  • A = 1, B = 1


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226.

Let f(x) = αxsinπx2    for x  21                      for x = 0

where αx is such that limx0αx = .

Then the function f(x) is contonuous at x = 0 if αx is chosen as

  • 2πx

  • 1x2

  • 2πx2

     

  • 1x


A.

2πx

Given,fx = αxsinπx2    for x  21                      for x = 0    ...iFor f(x)to be continuous at x = 0              limx0fx = f0From Eq (i),   f(0) = 1 For f(x)to be continuous at x = 0,limx0αxsinπx2 =1The above limlt is equal to 1, when                        αx = 2πxi.e., limx0sinπx2πx2 = 1      limx0 sinθθ = 1Hence, option  (a) αx = 2πx is correct


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227.

Let the equation ofa curve is given in implicit form as y = tanx + y. Then d2ydx2 in terms of y is

  • 21 + y2y6

  • - 21 + y2y6

  • - 21 + y2y5

  • 21 + y22y5


228.

The function f(x) = xtan-11x for x  0, f(0) = 0 is

  • differentiable at x = 0

  • neither continuous at x = 0 nor differentiable at x = 0

  • not continuous at x = 0

  • continuous at x = 0 but not differentiable at x = 0


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229.

If function f(x) = xsin1x; x  0a;           x = 0 is continuous at x = 0, then the value of a is

  • 0

  • 1

  • - 1

  • None of these


230.

At which point the function f(x) = x2x, where [.] is greatest integer function, is discontinuous ?

  • Only positve integers

  • All postive and negative integers and (0,1)

  • all rational numbers

  • None of these


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