Here's the question you clicked on:
Study23
Limits help (kind of forgot...) Click here to see function
\[ \huge \lim_{x \rightarrow 2} \frac{(x-3)(x+2)}{(x-2)}.\]
How can I simplify the denominator so that it doesnt give me a 0..?
numerator is not zero, so go fish
? Wouldn't it be a a denominator of 0, which is a "no-no"?
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
No, We haven't learned about that yet
l'hopital works for \(\frac{0}{0}\) in any case you didn't get there yet i am sure
So, @satellite73 would the limit be DNE ?
Because my teacher always says to only substitute directly when the denominator is not equal to zero...
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
That makes a lot of sense @satellite73! Thanks so much!!