Question Number 100036 by bobhans last updated on 24/Jun/20

f(x)= (((√(1+sin 2x))−(√(1−2sin x)))/x)  g(x) = 2x+ (√(2x)) . find lim_(x→0)  g(f(x))

Answered by john santu last updated on 24/Jun/20

lim_(x→0)  g(f(x)) = g(lim_(x→0)  f(x))  = g(lim_(x→0) (((√(1+sin 2x))−(√(1−2sin x)))/x))  = g(lim_(x→0)  (((1+((sin 2x)/2))−(1−((2sin x)/2)))/x))  =g(lim_(x→0) (((1/2)sin 2x+sin x)/x)) = g(2)  = 2.2 + (√(2.2)) = 4 + 2 = 6 ■