Question

Help http://prntscr.com/3hqz5i

Answer 1

\[\Large \lim_{x \rightarrow -3^+} f(x)\]basically means the value of f(x) when x approaches to -3 from right side.

do you know what it approaches to?

Answer 2

As it approaches -3, f(x) decreases. Right? So it does exist and it would it be D? Negative real numbers?

Answer 3

well yeah. when x approaches to -3 from right sides, f(x) does decrease, all way down to negative infinity.

Just so you know, infinity is not really real number.

Answer 4

Yeah I meant negative infinity. sorry.
I have another question looking for \[\lim_{x \rightarrow -3^-}\]
Would this one be positive infinity?

Answer 5

Yes

Answer 6

Okay one more. I just want to double check this one. \[\lim_{x \rightarrow 3} f(x)\]

This one doesnt exist right?

Answer 7

actually it does exists, because from both sides, it approaches same value.

Answer 8

\[\lim_{x \rightarrow -3} f(x) \space \nexists\]

Answer 9

∄ means "does not exist"

Answer 10

is that clear?

Answer 11

Sorta. I had someone tell me on here that it didnt exist, but his explanation wasnt clear. I get that both side approach the same value, which is six. http://prntscr.com/3hr9di. It would be D right?

Answer 12

I dont see that f(x) approaches 6 as x approaches 3 from both sides. B would makes sense.

Answer 13

from both sides, it approaches infinity.

Answer 14

Yeah I just saw that. I was looking at the last y value on the graph for some reason. Dont know what I was thinking. So as x approaches 3, f(x) increases infinity, which would be b(like you said)

Answer 15

Thank you for your help today!

Answer 16

welcome!