Question Number 105114 by john santu last updated on 26/Jul/20

lim_(x→0) ((2−((1−sin  ^2 (3x)))^(1/3) −((1−sin  ^2 (2x)))^(1/3) )/x^2 )

Answered by bemath last updated on 26/Jul/20

lim_(x→0) ((2−(1−((sin  ^2 (3x))/3))−(1−((sin  ^2 (2x))/3)))/x^2 )  lim_(x→0) (((1/3)(sin  ^2 (3x)+sin ^2 (2x)))/x^2 ) =        →(1/3)(9+4) = ((13)/3)

Answered by OlafThorendsen last updated on 26/Jul/20

lim_(x→0) ((2−((1−9x^2 ))^(1/3) −((1−4x^2 ))^(1/3) )/x^2 )  lim_(x→0) ((2−(1−3x^2 )−(1−(4/3)x^2 ))/x^2 )  = ((13)/3)