Question

Find the limit of the function algebraically.

Answer 1

Hint* factor the numerator

Answer 2

i tried doing this myself and got -6 but im not that good with limits so i want to double check

Answer 3

(x+6)(x-6)

Answer 4

Use `a²-b²=(a-b)(a+b)` and cancel the (x+6) on top and bottom. Then plug in -6 for x.

Answer 5

-12 (:

Answer 6

No -6 would be incorrect...

And yes that is the correct factorization

So now

\[\large \lim_{x \rightarrow -6}\frac{\cancel{(x + 6)}(x - 6)}{\cancel{x + 6}}\]

So we are left with

\[\large \lim_{x \rightarrow -6} x - 6\]

Just plug in -6 for 'x' and you get?

Answer 7

There we go!

Answer 8

\[\lim_{x \rightarrow -6}~\frac{x^2-36}{x+6}\]\[\lim_{x \rightarrow -6}~\frac{(x+6)(x-6)}{(x+6)}\]\[\lim_{x \rightarrow -6}~\frac{\cancel{ (x+6)}(x-6)}{\cancel{ (x+6) } }\]\[\lim_{x \rightarrow -6}~x-6\]\[\lim_{x \rightarrow -6}~(-6)-6\]\[\lim_{x \rightarrow -6}~-12\]

Answer 9

questions ?