### Mathematics - Limits

#### 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