Question

If lim _(x→0) ((x² + x + 1)/(x + 1) – ax – b) = 4, then find the values of a and b.

Answer 1

Given lim _(x→0) ((x² + x + 1)/(x + 1) – ax – b) = 4

It is possible only when 

⇒ (1 – a) = 0, (1 – a – b) = 4 

⇒ a = 1, a + b = –3 

⇒ a = 1 and b = – 4