## Study23 3 years ago Limits help (kind of forgot...) Click here to see function

1. Study23

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

2. Study23

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

3. satellite73

numerator is not zero, so go fish

4. hartnn

directly put x=2

5. satellite73

i.e. no limit

6. Study23

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

7. satellite73

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

8. satellite73

no

9. Study23

No, We haven't learned about that yet

10. satellite73

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

11. Study23

So, @satellite73 would the limit be DNE ?

12. Study23

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

13. satellite73

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

14. Study23

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