displaystyle lim x arrow 0+ log tan x( tan 2 x) is equal to

Question

displaystyle lim x arrow 0+ log tan x( tan 2 x) is equal to (A) 1 (B) -1 (C) 0 (D) None of these

Tardigrade Admin · Accepted Answer

displaystyle lim x arrow 0+ log tan x( tan 2 x) = displaystyle lim x arrow 0+ ( log ( tan 2 x)/ log ( tan x))((∞/∞). form ) = displaystyle lim x arrow 0+ ((1/ tan 2 x)(2 sec 2 2 x)/(1) tan x( sec 2 x)) [Using L' Hospital's rule] = displaystyle lim x arrow 0+ (2 sin x cos x/ sin 2 x cos 2 x)= displaystyle lim x arrow 0+ (2 sin 2 x/ sin 4 x)((0/0). form ) = displaystyle lim x arrow 0+ (4 cos 2 x/4 cos 4 x)=1. [Using L' Hospital's rule]

Q. x→0+lim​logtanx​(tan2x) is equal to

1

-1

0

None of these

x→0+lim​logtanx​(tan2x) =x→0+lim​log(tanx)log(tan2x)​(∞∞​ form ) =x→0+lim​tanx1​(sec2x)tan2x1​(2sec22x)​ [Using L' Hospital's rule] =x→0+lim​sin2xcos2x2sinxcosx​=x→0+lim​sin4x2sin2x​(00​ form ) =x→0+lim​4cos4x4cos2x​=1. [Using L' Hospital's rule]

Q. $x \to 0^{+} lim lo g_{t a n x} (tan 2 x)$ is equal to