Jika lim x→5 { x-\(ax + b }/x^2 - 25 = 1/25, nilai dari a + b? \(ax + b maksudnya akar ax + b

Lim (x - √(ax + b)) / (x^2 - 25)
1) jika kita langsung substitusi x = 5 ke limit aljabar maka hasilnya 0/0
(5 - √(5a + b))/(5^2 - 25) = 0/0
=> 5 - √(5a + b) = 0
=> - √(5a + b) = -5
=> 5a + b = 25

2) jika kita turunkan (L'HOSPITAL​) dan substitusi x = 5 maka hasilnya 1/25
Lim (x - (ax + b)^1/2) / (x^2 - 25) = 1/25
Lim (1 - (1/2) (ax + b)^-1/2 . a) / (2x) = 1/25
Lim (1 - a/(2√(ax + b)) / (2x) = 1/25
(1 - a/(2√(5a + b)) / 2(5) = 1/25
(1 - a/(2√25)) / 10 = 1/25
(1 - a/10) / 10 = 1/25
(10 - a)/100 = 1/25
(10 - a) = 4
6 = a

5a + b = 25
5(6) + b = 25
b = -5

Jadi a + b = 6 + (-5) = 1