Question

Find the limit, if it exist, of lim(x-->-4) (a^3+64)/a+4

Answer 1

factor top and bottom, cancel (x+4) on top and bottom, and then plug in -4 for x.

Answer 2

not x, but a... you get the idea.

Answer 3

@SolomonZelman How do you factor x^3 + 64? Can you please explain?

Answer 4

\[\LARGE \lim_{x \rightarrow -4}~ \frac{a^{3}+64}{a+4}\]\[\LARGE \lim_{x \rightarrow -4}~ \frac{a^{3}+4^{3}}{a+4}\]\[\LARGE \lim_{x \rightarrow -4}~ \frac{(a+4)(a^{2}-4a+4^{2})}{a+4}\] can you finish it from here ?

Answer 5

But would a be -4???

Answer 6

Well, I am thinking that you meant to write it, as with a--> -4

Answer 7

So, a is -4 (not exactly, but roughly speaking, "a approaches -4"

Answer 8

So it would be (-4+4) (-4^2-4*-4+4^2)/-4+4?

Answer 9

No no....

1) Do you see how I factored the top ?
2) If you do, then cancel (a+4) on top and bottom.
3) AFTER doing #2, plug in -4 instead of a

Answer 10

oooh okay so (-4^2+4*-4+4^2) = 16???

Answer 11

YES, you are correct!

Can we do another similar to this one, to make sure? It won't take long .

Answer 12

Yes. Please! What about lim x-->0 sqrtx+4-2/x

Answer 13

\[\huge\color{blue}{ \lim_{x \rightarrow0} \frac{\sqrt{x+4}-2}{x} }\] right ?

Answer 14

Yes.