Question

Is the function attached inside continuous for all of x?

**answer choices attached inside too:)

please explain!! thanks! :)

Answer 1

function!!

Answer 2

answer choices A,B,C,D,E from top to bottom :)

Answer 3

any idea ?

Answer 4

ermm not sure if i'm understanding this correctly, but would the limit be 6? :/

Answer 5

the limit as x->0 is what number you get as x gets closer to 0 (but does not reach 0)
when x is not 0, you use the first equation
5x/x = 5 even if x is 0.000000001 (tiny number)

you get the same limit from either direction, so the limit of this function as x->0 is 5

Answer 6

ohhh okay i see... i didn't apply it to the right equation haha

so it would be choice B right? where it says it's continuous and the limit equals 5?

Answer 7

any time you see jumps (here at x=0 you get f(0)= 6 ) you should suspect not continuous. (Continuous means you can draw it without lifting your pencil off the paper)

you have lim x->0 f(x) =5 but on the other hand f(0)= 6
that is not continuous

Answer 8

ohhh okay... so would it be answer choice D?

Answer 9

yes, D

Answer 10

awesome!! thank you!! :)

Answer 11

yw