If `lim_(xrarr0)((cotx)(e^(x)-1)-cos^(2)x)/(sinx)=K,Kepsilonr` then find the value of `[K+11/7]`, where `[.]` represents the greatest integer function.

Answer

2

Explanation

`lim_(xrarr0)(cotx(e^(x)-1)-cos^(2)x)/(sinx)`
`=lim_(xrarr0)(e^(x)-1-cosxsinx)/(sin^(2)x)`
`=lim_(xrarr)(e^(x)-1-1/2sin2x)/(x^(2))`
`=lim_(xrarr0)([x+(x^(2))/2-1/2(2x-((2x)^(3))/(3!))])/(x^(2))=1//2=k`
`implies[K+11/7]=[29/14]=2`