Question

Lim @ -2 (h^3+8)/(h+2)

Answer 1

make h very large
function becomes - 2 h^3/ h = -2h^2

Answer 2

lim as h --> -2 ?

The difficulty is caused because putting -2 into the numerator will cause division by 0.

I would say to factor h^3 + 8. h^3 + 8 = (h+2)(h^2 - 2h + 4)

Then, the h + 2 in the numerator and denominator will cancel out. So, this is a removable discontinuity. If you were to graph it, you would see that there would be a "hole" in the graph of the function when h= -2, but that the limit as you approach -2 is the same, whether you approach it from left or right, which means you can find the limit.

After canceling out the h + 2, you will be left with h^2 - 2h + 4 . Now, substitute -2 for h. (-2)^2 - 2(-2) + 4 = 12 So, 12 should be your limit as h approaches -2. I hope this was helpful!