Infinite Limits?

Question

lim
x--> -8+ 2x/ x+8

Can anyone explain to me HOW to get this awnser?

Answer 1

I assume you mean

lim [2x / (x + 8)]
x -> -8+

If we plug in -8, we get the form [-16/0]. Since this is a one-sided limit, we're either going to get infinity or -infinity. It's going to be either or, so all we have to do is test *any* value to the right of -8. If we get a positive value, the answer is going to be infinity. If a negative value, it's going to be -infinity.

Test x = -7. Then we get -14 / (1) = -14.
That means our answer is -infinity.

The key thing to note here is recognizing the form [a/0], for a not equal to 0. For one-sided limits, we're either going to get infinity or negative infinity, and all we have to do is test a single value close to the limit x is approaching (in our case, it was -8, so we chose a close value, -7).

Answer 2

we know x is approaching -8 from the right

subsitute -8 into equation which makes denominator 0 and threfore DNE, but try a number a little greater than -8 such as -7.99 because it is coming from the right, therefore

2(-7.99)/-7.99+8= -/+= -infinty

puggy is correct but it need not always be the case that a one-sided limit is +-infinty,

such as lim x approaching -1 from the right of the funtion x^2+2=

lim x approaching -1 from the left of the function x^2+2= 3

Answer 3

You should know from graphing rational functions that this goes asymptotic at x = -8, and it has a horizontal asymptote at y = 2. Since your limit approaches -8 from above, plug in x = -7. You get -14, so you know on that side of the asymptote the function is approaching -∞.