If lim x → 1 x 2 - a x + b x - 1 = 5 , then a + b is equal to:

Step-by-step solution

Given L = lim x → 1 ⁡ x 2 - a x + b x - 1 = 5 As x → 1 , the denominator becomes zero, hence for finite limit, the numerator must also approach to zero as x → 1 ⇒ 1 - a + b = 0 ⇒ b = a - 1       … ( 1 ) Now L = l i m x → 1 x 2 - a x + b x - 1   0 0 form By using L'Hospital Rule, ⇒ L = l i m x → 1 2 x - a 1 ⇒ L = l i m x → 1 2 x - a 1 = 5 ⇒ 2 - a = 5   ⇒ a = - 3 From the equation 1 , we get ⇒ b = a