Question

If limx> a[f(x)+g(x)] = 2 and lim x>a [f(x)-g(x)] = 1. Find lim x>a [f(x)g(x)].

Answer 1

Do you know the properties of limits?

Answer 2

Yes. But I'm confused what to do with this question.

Answer 3

\[\lim_{x \rightarrow a}[f(x)+g(x)]=\lim_{x \rightarrow a}f(x)+\lim_{x \rightarrow a}g(x)\]
\[\lim_{x \rightarrow a}[f(x)-g(x)]=\lim_{x \rightarrow a}f(x)-\lim_{x \rightarrow a}g(x)\]
\[\lim_{x \rightarrow a}[f(x)g(x)]=\lim_{x \rightarrow a}f(x)∙\lim_{x \rightarrow a}g(x)\]
There are of course more properties but these are the three you need to solve this problem.

Answer 4

Do you want a hint?

Answer 5

Yes please!

Answer 6

Sorry about that. I was typing and the stupid server keeps resetting. Give me a second to type it again.

Answer 7

It's okay! Yea the server has been very glitch today ):

Answer 8

Hint: Let\[\lim_{x \rightarrow a}f(x)=m\]and\[\lim_{x \rightarrow a}g(x)=n\]Do you understand what to do next?

Answer 9

I think so.... i will retry the question. Thank you very much!

Answer 10

I'll wait. Show me your work.

Answer 11

Can you show me the next step using this hint and the properties of limits?

Answer 12

\[\lim_{x \rightarrow a} f(x) = \lim_{x \rightarrow a} (\frac{ 1 }{ 2 } [f(x)+g(x)] - [\frac{ 1 }{ 2 } f(x)-g(x)]\]

Answer 13

sorry the minus between the two functions is suppose to be a plus*

Answer 14

No, I meant that\[\lim_{x \rightarrow a}f(x)+\lim_{x \rightarrow a}g(x)=2\]m + n = 2 (equation 1)\[\lim_{x \rightarrow a}f(x)-\lim_{x \rightarrow a}g(x)=1\]m - n = 1 (equation 2)

Now solve for m and n first. What do you get?

Answer 15

n=1/2 & m=5/2*

Answer 16

Yes m = 1/2 but n is incorrect. Please try again.

Answer 17

Sorry for a delay in responding but some idiot keeps harassing by sending me improper messages.

Answer 18

It's okay. Is there no option to block them?

Answer 19

I reported him so let's see if they do anything about it.

Answer 20

is m = 3/2?

Answer 21

Yes sorry I meant m = 3/2 and n = 1/2. Sorry I'm trying to focus but this person just doesn't stop.

Answer 22

Beset thing to do is not reply to him cause you're just feeding him to go on and on.

Answer 23

You're absolutely right.

Answer 24

So do you know the next step?

Answer 25

would you use the third limit property (from above) and multiply the two?

Answer 26

Actually the final answer now that you have solved the individual limits.

Answer 27

Yes! Go ahead.

Answer 28

Therefore the product of these limits is?

Answer 29

3/4

Answer 30

Beautiful!! Excellent work!! So do you now understand the concept of solving these types of problems?

Answer 31

Yes, I do. thank you very much!! My prof explained it very complicated... so I didn't really understand it. Really appreciate the help!

Answer 32

Absolutely any time! I have to log out now. That's what I said after helping the last person as well LOL but I really do have to go. I'll be back in a few hours maybe, so if you need me thensimply message me and I will definitely help you as soon I get back. Take care!

Answer 33

LOL don't worry that happens to everyone. Thanks once again!!! (:

Answer 34

Welcome! Bye for now!