Question

lim as x-->pi/2- of (tanx)/(3/(2x-pi))

Answer 1

is it\[\lim_{x \rightarrow \pi/2^{-}}\frac{ tanx }{ \frac{ 3 }{ 2x-\pi } }\]

Answer 2

then u can start with\[\lim_{x \rightarrow \pi/2}\frac{ tanx(2x-\pi) }{ 3 }=1/3*\lim_{x \rightarrow \pi/2}\frac{ 2x-\pi}{ cotx }\]

Answer 3

then use L'hospital i.e diffrentiate denominator and numerator once wrt x

Answer 4

u;ll get\[=1/3*\lim_{x \rightarrow \pi/2}\frac{ 2 }{ -cosec^2x }=-2/3*\frac{ 1 }{cosec^2(\pi/2) }\]

Answer 5

cosec(pi/2)=1
so finally
lim=-2/3
feel free to ask if u have any doubt @chomchommit1996