Question

Without graphing or using L'Hopital's Rule, how do you find the limit of (x+6)/(x^2-6x+8) as x approaches 4-?

Answer 1

Here, factor the denominator.

Answer 2

(x+6)/((x-4)(x-2))

Answer 3

what happens when you plug in \(3.99999\) an \(4.00001\)?

Answer 4

Here, as you approach from the left, the (x-4) term is the one that is interesting.

Answer 5

It should be noted that you can't use L'Hopital's Rule here anyway, because you do not have an indeterminate form. \((4+6) \neq 0\).

Answer 6

when x-> 4-
(x-4) is positive or negative ?

Answer 7

@hartnn Meaning when x approaches 4 from the left. I think the answer is negative infinity. Thanks guys.

Answer 8

That's it.

Answer 9

yup, thats correct, when it approaches from positive side, it would be \(+\infty\)
welcome ^_^