Question

When do you "plug in and simplify" to find a limit?

Answer 1

when the limit exists?

Answer 2

hmm

Answer 3

would you like an example?

Answer 4

yes please

Answer 5

\[\huge \lim_{x \rightarrow 1} \quad \frac{x^2 - 1}{x-1}\]
try plugging in 1 into x

Answer 6

undefined

Answer 7

could it be when the function us continuis?

Answer 8

continuous

Answer 9

could it be what?

Answer 10

when the function is continuous

Answer 11

yeah...could be what?

Answer 12

you said could "it" be when the function is continuous

what is that "it"?

Answer 13

im going to explain my point...

in the example i gave when you plug in immediately you will get undefined

but if you simplify it first
\[\lim_{x\rightarrow 1} \quad \frac{(x+1)\cancel{(x-1)}}{\cancel{(x-1)}}\]
so therefore you can get \[\lim_{x\rightarrow} x+ 1 \implies 1 + 1 \implies 2\]
do you get that?

Answer 14

yes

Answer 15

great :)

Answer 16

so you can plug in and simplify when the function is continuos?

Answer 17

when the function is continuous yes :)

but in this case it is not continuous so you have to simplify first

Answer 18

got it thanks!