Question

Finding the limit algebraically? Medal award.
lim x^2 - 16 / x + 4
x -> -4

Answer choices :
1
-8
does not exist
-4

I plugged in -4 and got zero for the numerator and denominator...so I chose "does not exist"
But that answer is incorrect. What am I doing wrong?
Thanks for any help!!

Answer 1

There is a solution :)

Answer 2

Try factoring the numerator

Answer 3

okay! so (x -4)(x + 4)

Answer 4

\[\lim_{x \rightarrow -4} \frac{(x+4)(x-4)}{x+4} \\ \\ \lim_{x \rightarrow -4} \frac{\cancel{(x+4)}(x-4)}{\cancel{(x+4)}} \\ \\ \lim_{x \rightarrow -4}x-4\]
now substitute x=-4 into that

Answer 5

oh!! so the answer would be -8!

Answer 6

Yes!

Answer 7

Thanks so much!! Never thought of that!

Answer 8

@.Sam. nice use of \(\cancel{a}\)

Answer 9

most of the limit problems involves factoring and playing with the terms, you just have to look at it carefully first :)