Question Number 104667 by bobhans last updated on 23/Jul/20

lim_(x→0)  [(3^(πx) /(tan x)) − ((cos ^2 x)/(sin x))] ?

Answered by bramlex last updated on 23/Jul/20

lim_(x→0) ((3^(πx) .cos x)/(sin x))− ((cos ^2 x)/(sin x)) =  lim_(x→0)  ((cos x)/(sin x)) {3^(πx) −cos x } =   lim_(x→0) ((x.cos x)/(sin x)) {((3^(πx) −cos x)/x)} =  lim_(x→0)  cos x. (x/(sin x)) {((3^(πx) −1+1−cos x)/x)}=  1 ×lim_(x→0)  {((3^(πx) −1)/x) + ((1−cos x)/x)} =  1×lim_(x→0)  {((π.ln (3).3^(πx) )/1) + 0 } =  π.ln (3) ★

Commented bybobhans last updated on 23/Jul/20

very nice ! ⌣^o  !