limits

not defined

see LHL = - RHL

if u see expansion of cotx itll be clearer

cot(x)=1/x-x/3-(x^3)/45-(higher powers of x)

hmm now i think 0 is the ans

one more question ..why is dat sm1 who got good rank in iit..takes so much time..and sm1 like me who far below than bad in iit could answer that in seconds ........................

dont take it personally ........i was just amazed!

all the best.

becoz top ranker may be i think analyzes all aspects and gets a really confident answer...........having analyzed all perspectives of the asked problem[1]

toppers will have high radiantly thinking brain.

\lim_{x\rightarrow 0}(cotx-\frac{1}{x})
\lim_{x\rightarrow 0}(\frac{x-tanx}{xtanx})

\lim_{x\rightarrow 0}(\frac{x-tanx}{x^2tanx/x})

\lim_{x\rightarrow 0}(\frac{1-sec^2x}{2x}) (LH rule)

\lim_{x\rightarrow 0}(\frac{-tan^2x}{2x})

\lim_{x\rightarrow 0}(\frac{-x^2tan^2x/x^2}{2x})

\lim_{x\rightarrow 0}\frac{-x}{2} = 0