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Question

Question: \((fof)(2)\) is...

(fof)(2)(fof)(2) is

A

11/4

B

¾

C

½

D

None of these

Answer

¾

Explanation

Solution

lim⁡x→π41−cot⁡3x2−cot⁡x−cot⁡3x\lim _ { x \rightarrow \frac { \pi } { 4 } } \frac { 1 - \cot ^ { 3 } x } { 2 - \cot x - \cot ^ { 3 } x }

= lim⁡x→π4(1−cot⁡x)(1+cot⁡x+cot⁡2x)(1−cot⁡x)(cot⁡2x+cot⁡x+2)\lim _ { x \rightarrow \frac { \pi } { 4 } } \frac { ( 1 - \cot x ) \left( 1 + \cot x + \cot ^ { 2 } x \right) } { ( 1 - \cot x ) \left( \cot ^ { 2 } x + \cot x + 2 \right) }

= lim⁡x→π41+cot⁡x+cot⁡2xcot⁡2x+cot⁡x+2=34\lim _ { x \rightarrow \frac { \pi } { 4 } } \frac { 1 + \cot x + \cot ^ { 2 } x } { \cot ^ { 2 } x + \cot x + 2 } = \frac { 3 } { 4 }