Limit of (ax^2-b)/(x-2)=4 as x approaches to 2 find the value of a and b?
1 Answer
Jan 25, 2018
# a=1 \ \ # and# \ \ b=4 #
Explanation:
We require that:
# L = lim_(x rarr 2) (ax^2-b)/(x-2)=4 #
As the denominator is zero when
# L = lim_(x rarr 2) ((x-alpha)(x-2))/(x-2) #
# \ \ = lim_(x rarr 2) (x-alpha) #
# \ \ = 2-alpha #
But we know that
# 2-alpha = 4 => alpha=-2#
Given this we can now write the numerator as:
# ax^2-b -= (x+2)(x-2) = x^2-4 #
And by comparing coefficients we have:
# a=1 \ \ # and# \ \ b=4 #