What is the maximum value of sinxcosx ? from Mathemati

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 Multiple Choice QuestionsMultiple Choice Questions

31.

What is the value of limx0sinx°tan3x°

  • 14

  • 13

  • 12

  • 1


32.

What is  limx03x + 3 - x - 2x = ?

  • 0

  • - 1

  • 1

  • limit does not exist


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33.

What is the maximum value of sinxcosx ?

  • 2

  • 1

  • 12

  • 22


C.

12

Now, we can write as

 sinxcosx = 12sin2xTo find out maximum of the sinxcosxdifferentiate it w.r.t x and then equate it to 0.ddx12sin2x = 12ddxsin2x = 122cos2x = 0cos2x = 0cos2x = cos2, where n = 1, 3, 5 ... odd integer2x = 2x = 4, where, n = 1, 3, 5 ...odd integer

For maximum value n = 1, 5, 9 because 3, 7... will result in minimum value

 sinπ4cosπ4 = 12


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34.

The value of ordinate of the graph of y = 2 + cos(x) lies in the interval

  • [0, 1]

  • [0, 3]

  • [ - 1, 1]

  • [1, 3]


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35.

What is limx0sinxlog1 - xx2 = ?

  •  - 1

  • Zero

  •  - e

  • 1e


36.

If limx1x4 - 1x - 1 = limxkx3 - k3x2 - k2 where k  0, then what is the value of k ?

  • 23

  • 43

  • 83

  • 4


37.

What is limx1x + x2 + x3 - 3x - 1 = ?

  • 1

  • 2

  • 3

  • 6


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