If f is defined by fx = x 

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 Multiple Choice QuestionsMultiple Choice Questions

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121.

If f is defined by fx = x        for 0  x  12 - x  for x  1, then at x = 1, fx is

  • continuous and differentable

  • Continuous but not differentiable

  • discontinuous but differentiable

  • Neither continuous nor differentiable


B.

Continuous but not differentiable

LHL                      RHL                                  f1           limx1- x                 limx1+ 2 - x                   = 2 - 1    limh1- h                 limh1+ 2 - h                   = 1  LHL = RHL = f1                                               Hence, fx is continuous at x = 1  LHD                               RHD                                       limx1-fx - f1x - 1   limx1+fx - f1x - 1limx1-x - 1x - 1      limx1+2 - x - 1x - 1= 1                             = - 1              LHD  RHD                                                Hence, fx is discontinuous at x = 1


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122.

limx06x - 3x - 2x + 1x2 = ?

  • loge2loge3

  • loge5

  • loge6

  • 0


123.

Define fx = x2 + bx + c, x < 1x, x  1 If fx is differentiable at x = 1, then b - c = ?

  •  - 2

  • 0

  • 1

  • 2


124.

limn1k + 2k + 3k + ... + nknk + 1 = ?

  • 1k

  • 2k + 1

  • 1k + 1

  • 2k


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125.

limx0 1 - cos2x3 + cosxxtan4x = ? 

  •  - 14

  • 12

  • 1

  • 2


126.

An angle between the curves x2=3y and x2 + y2 = 4 is

  • tan-153

  • tan-153

  • tan-123

  • π3


127.

If p(x) be a polynomial of degree three that has a local maximum value 8 at x = 1 and a local minimum value 4 at x = 2; then p(0)is equal to

  •  - 24

  •  - 12

  • 6

  • 12


128.

If a function f(x) defined by

fx = aex + be - x, - 1  x < 1cx2, 1  x  3ax2 2cx, 3 < x  4be continuous for some a, b, c  R and f,0 + f'2 = e, then the value of a is :

  • 1e2 - 3e + 13

  • ee2 - 3e + 13

  • ee2 - 3e - 13

  • ee2 + 3e + 13


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 Multiple Choice QuestionsShort Answer Type

129.

If limx1x +x2 + x3 +... + xn - nx - 1 = 820, n  N then the value of n =?


 Multiple Choice QuestionsMultiple Choice Questions

130.

limx0tanπ4 + x1x = ?

  • 2

  • 1

  • e

  • e2


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