The value of limx→∞a2x2 + ax +&nbs

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 Multiple Choice QuestionsMultiple Choice Questions

41.

The value of limnnn2 + 12 + nn2 + 22 + ... + nn2 + n2 is

  • π4

  • log2

  • 0

  • 1


42.

The value of limn1n + 1 + 1n + 2 + ... + 16n is

  • log2

  • log6

  • 1

  • log3


43.

limxπ2acotx - acosxcotx - cosx

  • logeπ2

  • loge2

  • logea

  • a


44.

The value of limx252 - x is

  • 102

  • does not exist


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45.

The value of limx2e3x - 6 - 1sin2 - x

  • 32

  • 3

  • - 3

  • - 1


46.

dndxnlogx is equal to

  • n - 1!Xn

  • n !Xn

  • n - 2!Xn

  • - 1n - 1n - 1!Xn


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47.

The value of limxa2x2 + ax + 1 - a2x2 + 1 is

  • 12

  • 1

  • 2

  • None of these


A.

12

Given, limxa2x2 + ax + 1 - a2x2 + 1= limxa2x2 + ax + 1 - a2x2 - 1a2x2 + ax + 1 + a2x2 + 1= limxaxa2 + ax + 1x2a2 + 1x2= aa2 + a2 = a2a = 12


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48.

limx01 - cos2xsin5xx2sin3x equals

  • 103

  • 310

  • 65

  • 56


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49.

limx1 - 4x - 13x - 1 is equal to

  • e12

  • e- 12

  • e4

  • e3


50.

limx0ax - bxex - 1 is equal to 

  • logeab

  • logeba

  • logeab

  • logea + b


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