If [ _x 1 x^2 - ax + b x - 1 = 5], then a + b is equal to :

Question

If $$\mathop {\lim }\limits_{x \to 1} {{{x^2} - ax + b} \over {x - 1}} = 5$$, then a + b is equal to :

Accepted Answer

$$\mathop {\lim }\limits_{x \to 1} {{{x^2} - ax + b} \over {x - 1}} = 5$$

$$ \Rightarrow $$ ${(1)^2} - a(1) + b = 0$

$$ \Rightarrow $$ $1 - a + b = 0$$ \Rightarrow $$ $a - b = 1\,\,......(1)$$

Now 'L' hospital rule

2x - a = 5

$$ \Rightarrow $$2 - a = 5 ($$ \because $$ x = 1)

$$ \Rightarrow $$ a = - 3

By putting a = -3 in (1)

$$ \Rightarrow $$ b = -4

$$ \therefore $$ a + b = -7

Solutions · 1