Mathematics - Limits

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Question - 1

\(\underset { X\ \rightarrow \ 1 }{ lim } \)[x - 1], where [.] is greatest integer function, is

  • A 1
  • B 2
  • C 0
  • D does not exist

Question - 2

If \(\underset { X \rightarrow 1 }{ lim } \)\({X^4-1\over X-1}=\underset{x \rightarrow k}{lim}{X^3-k^3\over X^2 - k^2},\)then the value of k is

  • A \(-8 \over 3\)
  • B \(5 \over 3\)
  • C \(-{5\over 3}\)
  • D None of these

Question - 3

\(\underset{x \rightarrow 1}{lim}(1-x^2)log_{x^2}2\) equal to

  • A log2
  • B log 3
  • C -log2
  • D -log3

Question - 4

The value of \(\underset{x \rightarrow \infty}{lim}{(X+2)!+(X+1)!\over (X+2)!-(X+1)!}\)is

  • A 1
  • B 2
  • C 3
  • D 4

Question - 5

The value of \(\underset{x \rightarrow 4}{lim}{|x-4|\over x-4}\)is equal to

  • A 3
  • B -2
  • C 1
  • D does not exist

Question - 6

\(\underset{x \rightarrow \infty}{lim}(\sqrt{n+\sqrt{n+}\sqrt{n-}{\sqrt{n}}})\)is

  • A log n
  • B n2
  • C \(1\over 2\)
  • D 1

Question - 7

\(\underset{a \rightarrow \infty}{lim}[{1\over 1-a}+{8\over 1-a^4}+...+{a^3\over1-a^4}]\)is equal to

  • A \(1\over3\)
  • B \(1\over4\)
  • C \(-{1\over3}\)
  • D \(-{1\over4}\)

Question - 8

The value of \(\underset{x\rightarrow {\pi\over4}}{lim}{2-cot x-cot^3x\over 1-cot^3x}\)is

  • A \(45\over3\)
  • B 1
  • C 0
  • D None of the above

Question - 9

Find the value of \(\underset{x\rightarrow 0}{lim}{sinx-2sin\ 3x+sin\ 5x\over x}\)

  • A -1
  • B 0
  • C 1
  • D 3

Question - 10

\(\underset{x\rightarrow \infty}{lim}({x+1\over x+2})^{2x+1}\)equal to

  • A e3
  • B e-3
  • C e-2
  • D e2
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