Question

Lim √x+6 - √2x+1 / x-5 = …
x→5

Answer 1

Lim(x→5) (√(x+6) - √(2x+1))/(x-5)
= lim(x→5) (√(x+6) - √(2x+1))/(x-5) x (√(x+6)+√(2x+1))/(√(x+6)+√(2x+1))
= lim(x→5) (x+6 - 2x-1) / (x-5)(√(x+6)+√(2x+1))
= lim(x→5) (-x+5) / (x-5)(√(x+6)+√(2x+1))
= lim(x→5) -(x-5) / (x-5)(√(x+6)+√(2x+1))   ; coret (x-5)
= lim(x→5) -1 / (√(x+6)+√(2x+1))               ; subtitusi x = 5
= -1 / (√11 + √11)
= -1 / (2√11)

rasionalkan:
= -(√11)/22