Question

Evaluate the limit:
(see attachment)

Answer 1

(1/x^2 - 1/4) * (x-1)/(x^2-3x+2) =
(4 - x^2) / 4x^2 * (x - 1) / { (x - 1)(x - 2) } =
(2 + x)(2 - x) / 4x^2 * 1 / (x - 2) =
-(2 + x) / 4x^2
lim x-> 2 -(2 + x) / 4x^2 = -(2 + 2) / (4 * 2^2) = -4 / 16 = -1/4

Answer 2

first factorise the quadratic polynomial down there ..and (x-1) gets cancelled ..
multiply and then apply L.Hospital rule .!