If fx = xtan-1x, then limx→1fx 

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 Multiple Choice QuestionsMultiple Choice Questions

111.

limx0 tanx - sinxx2 = ?

  • 0

  • 1

  • 12

  • - 12


112.

If f(x) = x + sinx for x  - π2, π2, then its left hand derivative at x = 0 is

  • 0

  • - 1

  • - 2

  • - 3


113.

If u = ux, y = siny + ax - y + ax2, then it implies

  • uxx = a2 . uyy

  • uyy = a2uxx

  • uxx = - a2 . uyy

  • uyy = - a2uxx


114.

limxx + 6x + 1x + 4 = ?

  • e4

  • e6

  • e5

  • e


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115.

The coordinates of the point P on the curve x = aθ + sinθ, y = a1 - cosθ, where the tangent is inclined at an angle π4 to x-axis, are

  • aπ4 - 1, a

  • aπ2 + 1, a

  • aπ2, a

  • (a, a)


116.

If f :- 2,  2  R is defined by fx = 1 + cx - 1 - cxx for - 2  x  0x + 3x + 1 for 0  x  2continuous on - 2,  2, then c is equal to

  • 23

  • 3

  • 32

  • 32


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117.

If fx = xtan-1x, then limx1fx - f1x - 1 = ?

  • π +34

  • π4

  • π + 14

  • π +24


D.

π +24

Given, f(x) = xtan-1x thenlimx1 fx - f1x - 1  00 form= limx1 f'x - 01Using L'Hospital rule= limx1x1 + x2 + tan-1x= 112 + 12 +  tan-11 = 12 + π4= 2 + π4 or π + 24


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118.

The value of c in the Lagrange's mean value theorem for f(x) = x - 2 in the interval [2, 6] is

  • 92

  • 52

  • 3

  • 4


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119.

If gx = xx for x> 2, then limx2 gx - g2x - 2 = ?

  •  - 1

  • 0

  • 1/2

  • 1


120.

limxπ22x - πcosx = ?

  • 0

  • 1/2

  •  - 2

  • 5


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