Question

How do you find the limit of `(2-x)/(x^2-4)` as `x->2^+`?

Answer 1

`lim_(x->2^+)(2-x)/(x^2-4)=-1/4`

Explanation:

Note that we can write the function as:

`(2-x)/(x^2-4)= - (x-2)/((x-2)(x+2))= -1/(x+2)`

In this way we eliminate the discontinuity for `x=2` and find that:

`lim_(x->2^+)(2-x)/(x^2-4)=lim_(x->2^+) -1/(x+2) =[-1/(x+2)]_(x=2)=-1/4`