Question

beginner calculus stuff right here..
find the limit as x approaches 3:
(x^2-x-6)/(x^2-6x+9)

Answer 1

(x-3)(x-2) / (x-3)(x-3)

Answer 2

cancel (x-3)

Answer 3

The numerator and denominator have the same degree, so the coefficients are the limit.

Answer 4

-5

Answer 5

(x-2)/(x-3)
as you approach 3 from right you get + infinity , if you approach from left you get - infinity

Answer 6

so inderterminant

Answer 7

it'll be 1

Answer 8

yes, ive done this, but the denominator is still equal to zero. How do i solve the equation so I can plug in a 3?

Answer 9

I am right, everyone else is wrong

Answer 10

u have to take the limit from above and below i'm pretty sure

Answer 11

and if you use L'Hospital's rule it comes out to 1

Answer 12

but if this is beginner stuff...just listen to imranmeah91 b/c he's correct

Answer 13

you can't use L' Hopital rule unless you have 0/0 or infnity/infinity

Answer 14

it is 0/0

Answer 15

(x-2)/(x-3)
1/0

Answer 16

before you factor it

Answer 17

you have to simplify it

Answer 18

the limit does not exist

Answer 19

using algebra/tricks there is no way to make this function "continuous" at 3
so the limit does not exist
and i say "continuous" because we aren't actually making the function continuous by finding the limit
does that make sense?

Answer 20

i guess we can say simplifying instead of making the function continuous maybe

Answer 21

but that is the goal if we cannot use direct substitution and there are no tricks that we can apply on the function that allow us to use direct substitution then the limit does not exist

Answer 22

that sounds better i think