Question

Limits help (kind of forgot...) Click here to see function

Answer 1

\[ \huge \lim_{x \rightarrow 2} \frac{(x-3)(x+2)}{(x-2)}.\]

Answer 2

How can I simplify the denominator so that it doesnt give me a 0..?

Answer 3

numerator is not zero, so go fish

Answer 4

directly put x=2

Answer 5

i.e. no limit

Answer 6

? Wouldn't it be a a denominator of 0, which is a "no-no"?

Answer 7

if you get a zero in the denominator, but not a zero in the numerator, then there is no limit
only when you get \(\frac{0}{0}\) can you continue if you get a zero in the denominator

Answer 8

no

Answer 9

No, We haven't learned about that yet

Answer 10

l'hopital works for \(\frac{0}{0}\) in any case you didn't get there yet i am sure

Answer 11

So, @satellite73 would the limit be DNE ?

Answer 12

Because my teacher always says to only substitute directly when the denominator is not equal to zero...

Answer 13

not applicable here
if you have a rational funciton, and you want to take the limit as x goes to some number, the first step is to plug in the number
if you get a number back, that is your answer
if you get \(\frac{a}{0}\) where \(a\neq 0\) there is no limit
if you get \(\frac{0}{0}\) there is more work to be done
factor and cancel
but in this case you get \(\frac{-4}{0}\) so forget it

Answer 14

That makes a lot of sense @satellite73! Thanks so much!!