lim √(x+2) (2x-1)- (x√2+1) x --> oo

Rumus
Lim √(ax^2 + bx + c) - √(px^2 + qx + r) = (b - q)/(2√a) dgn syarat a = p
x=>~

Lim √(x + 2)(2x - 1) - (x√2 + 1)
= Lim √(2x^2 - x + 4x - 2) - √(x√2 + 1)^2
= Lim √(2x^2 + 3x - 2) - √(2x^2 + 2√2 x + 1)
a = 2, b = 3, c = -2, p = 2, q = 2√2 , r = 1
Karena a = p maka (b - q)/(2√a)
= (3 - 2√2)/(2√2) . √2/√2
= (3√2 - 4)/4

= 1/4 (3√2 - 4)

= (3/4)√2 - 1