Question Number 104217 by bemath last updated on 20/Jul/20

lim_(x→0) ((tan (x+3)^2 −tan (9))/x) = ?

Answered by bemath last updated on 20/Jul/20

lim_(x→0) ((2(x+3)^1 sec ^2 (x+3)^2 )/1) =  2.3.sec ^2 (9) = 6 sec ^2 (9) ★

Answered by Dwaipayan Shikari last updated on 20/Jul/20

lim_(x→0) ((((sin(x+3)^2 )/(cos(x+3)^2 ))−((sin9)/(cos9)))/x)=lim_(x→0) ((sin((x+3)^2 −9))/(cos(x+3)^2 cos9)).(1/x)  (sin(x^2 +6x))=x^2 +6x  lim_(x→0) ((sin(x^2 +6x))/(cos(x+3)^2 cos9)).(1/x)lim_(x→0) ((x^2 +6x)/(cos^2 9)).(1/x)=6 sec^2 9★