Question

How do you evaluate `\lim _ { x \rightarrow 4} \frac { x ^ { 2} - 16} { 3x - 12}`?

Answer 1

`lim_(x->4) (x^2-16)/(3x-12) =8/3`

Explanation:

Factorize the numerator and denominator:

`(x^2-16)/(3x-12) = ((x+4)(x-4))/(3(x-4)) = (x+4)/3`

then:

`lim_(x->4) (x^2-16)/(3x-12) = lim_(x->4) (x+4)/3 = 8/3`