Question

.

Answer 1

Hi there!

Answer 2

Okay here is another property:
If\[
\lim_{x\to a}f(x)=L
\]and \[
\lim_{x\to a}g(x)=K
\]Then \[
\lim_{x\to a}f(x)\cdot g(x)=L\cdot K
\]

Answer 3

Give up, sorry!

Answer 4

Here is a test problem for this property.

Suppose: \[
\lim_{x\to 5}h(x)=20
\]Then what is \(L\) when:\[
\lim_{x\to 5}x^2h(x)=L
\]

Answer 5

Do you want me to show you how the property works?

Answer 6

what is h?

Answer 7

We don't know. Fortunately you don't need to know if you use the multiplication property.

Answer 8

What does it represent?

Answer 9

(the h)

Answer 10

It is some function.

Answer 11

Maybe \(h(x)=20\) or \(h(x)=4x\). We don't know. We just know the limit.

Answer 12

OK, and the problem was, ...

Answer 13

30?

Answer 14

Suppose: \[
\lim_{x\to 5}h(x)=20
\]Then what is \(L\) when:\[
\lim_{x\to 5}x^2h(x)=L
\]
You need to do them separately.

Answer 15

I mean the answer.

Answer 16

Do you want to do the problem, or would you like me to do it?

Answer 17

Which problem the 1st or the 2nd?

Answer 18

The second equation is the problem. The first equation is information that will help you do it.

Answer 19

For the 1st i think the answer is 30.
and for the second 8000?

Answer 20

What? There is only one problem.

Answer 21

I plugged in the 20 for x, looks kind of sillly though!

Answer 22

Okay, what you should do is this: \[
\lim_{x\to 5}x^2h(x) = \left(\lim_{x\to 5}x^2\right)\left(\lim_{x\to 5}h(x)\right) = \left(\lim_{x\to 5}x^2\right)\left( 20 \right)
\]

Answer 23

how do you come up with doing that?

Answer 24

Here is the multiplication property:\[
\lim_{x\to a}f(x)=L
\]and \[
\lim_{x\to a}g(x)=K
\]Then \[
\lim_{x\to a}f(x)\cdot g(x)=L\cdot K
\]
You can also write it as: \[

\left(\lim_{x\to a}f(x)\cdot g(x)\right)=\left(\lim_{x\to a}f(x)\right)\cdot \left(\lim_{x\to a}g(x)\right)
\]

Answer 25

I think I get it!

Answer 26

Can you complete the problem?

Answer 27

And plug in x then!

Answer 28

25? Not sure though!

Answer 29

Yep!

Answer 30

Now to answer the original problem, you have to multiply them together.

Answer 31

But in this answer I got, i got it for gf not for g or for f.
What is the difference b/w gf function, g function and f function?

Answer 32

They are just two functions multiplied together, that is all.

Answer 33

The whole answer is \[
\left(\lim_{x\to 5}x^2\right)(20) = (25)(20)=500
\]

Answer 34

(erased what i typed b/f...)
I understand!

Answer 35

Do you know about piece wise functions?

Answer 36

I understand the f(x) in this problem but how do you know the g(x), how do you know that the x there is 25?

Answer 37

(b/f we get to piece wise functions)

Answer 38

How do I know: \[
\lim_{x\to 5}x^2=25
\]Is this what you are asking?

Answer 39

in the g(x), just looked up to the previous replies... Yes I do!

Answer 40

I get this, I think!

Answer 41

(you need more medals, another question? I'm going to ask Rachel to give you a medal, she will do that favor for me!)

Answer 42

Sure, next question then.