Evaluate the limit, if it exists.lim[x → 2] (x^2 − 6x + 8)/(x − 2)

Answer 1

The key here is that you have a division by zero when you plug 2 into the equation. This means that we have one of the indeterminate forms we need to apply L'Hopital's Rule. The rule states that you differentiate the numerator and denominator of the expression and then evaluate the result. The limit of the new expression will be the same as the limit of the original equation.

Differentiating the top and bottom we get

lim x->2 (2x-6)/1

Since we no longer have the division by zero which was causing problems we can plug 2 into the expression.

(2*2)-6=(-2)

So the limit of the expression is -2