Question

Use algebra to find the limit

lim f(x)
x->3+

when.....
rest drawn inside :)

Answer 1

would i be using 2x+1 for the right limit?

Answer 2

yes

Answer 3

what is the \(a=3\) supposed to mean? if you approach from \(3^+\) then I guess you have miswritten the lower limit am I correct?

Answer 4

nevermind, I have misread it myself (-: You're on the right track, pardon me.

Answer 5

oh it's based off of the format

lim f(x)
x-> a+

sorry i forgot to mention that haha i had already subbed it in :p

and okay, so would it become 2(3) + 1 = 6=1 =7 ?

Answer 6

yes

Answer 7

As you get closer and closer to 3 when approaching from the right, the y value on the graph gets closer and closer to 7

Answer 8

okay awesome! and so for

lim f(x)
x-> 3-

would i be using x^2 - 2 ?

Answer 9

ahh okay awesome! @Mertsj :)

Answer 10

yes

Answer 11

\(x \to 3^{-1}\) zest means that \(x\) approaches 3 from the left, therefore \(x \) is smaller than 3.

Answer 12

okay:)

so 3^2 -2 = 9 -2 = 7?

is that right? if so, that means that the entire limit is also 7 right?

Answer 13

and would this be the graph of the limit?

because it's continuous right?

Answer 14

That is both the right and left limit but notice that the function defines f(3) as 2.

Answer 15

It is not continuous because f(3) is NOT 7 according to what you posted earlier.

Answer 16

ohh f(3) would be 2?

so does this graph make more sense?

Answer 17

No. Because the graph approaches 7 from both the right and left.

Answer 18

ohh okay... hmm would it look something like this?

those are the only choices my teacher put on the sheet... :/