Question

Jika lim x menuju 2 x² - 4 / x² + ax + b maka a + b = ?

Answer 1

Verified answer

Jawab

lim ( x→ 2)  (x² - 4) / (x² + ax+ b) = 4

(i) bentuk 0/0 , untuk x = 2
 x = 2 → x²+ ax + b = 0
4 + 2a  + b = 0
2a + b = - 4
b = - 4 - 2a ....(i)

(ii) d'hospital
u = x² - 4 → u' = 2x
v = x² + ax + b → v' = 2x + a

untuk x = 2  →  u'./v' = 4
 2x/(2x + a) = 4
2(2) / (2.2 + a) = 4
4/ (4 + a) =4
4+ a = 1
a = - 3 ....sub ke  (i)  
b = -4 - 2a
b = -4 - 2(-3)
b = 2

nili a + b  = -3 + 2
a + b = - 1