Question Number 114543 by bemath last updated on 19/Sep/20

 lim_(x→0)  ((x^2  arctan (2x))/(x cos x+tan x)) ?

Answered by bobhans last updated on 19/Sep/20

lim_(x→0)  ((x^2  tan^(−1) (2x))/(x cos x+tan x)) = lim_(x→0)   ((2x^3 )/(x(1−(x^2 /2))+(x+(1/3)x^3 )))  = lim_(x→0)  ((2x^3 )/(2x−(1/6)x^3 )) = lim_(x→0)  ((2x^2 )/(2−(1/6)x^2 )) = 0

Answered by mathmax by abdo last updated on 19/Sep/20

by hospital theorem  we get  L =lim_(x→0)        ((2x arctanx+x^2 .(2/(1+4x^2 )))/(cosx −xsinx +1+tan^2 x)) =(0/2)=0