Question

.

Answer 1

I am here!

Answer 2

@wio please ask inkyvoyd to leave!

Answer 3

Yes, I have.

Answer 4

he messed like 3 of my threads up, and distracting me after all of that!

Answer 5

Okay, let me ask you a question about a limit.

Answer 6

Should I call a moderator, inkyvoyd?

Answer 7

ask about the limit,, please!

Answer 8

Here is a simple problem

Suppose:\[
\lim_{x\to 5}=x^2+x-9=L
\]What is \(L\)?

Answer 9

Need a hint?

Answer 10

Hold on!

Answer 11

Should i factor it?

Answer 12

No need.

Answer 13

yes, hint, please!

Answer 14

Okay in the past I said: \[
\lim_{x\to 2}x+1=3
\]And this is because sometimes the limit the same as the actual output of the function.

Answer 15

So i should eliminate/solve for x?

Answer 16

No. You can actually just substitute \(x=5\).

Answer 17

why 5, how sshould i come up with substituting 5?

Answer 18

Oh, I see b/c it is limited to 5!

Answer 19

21?

Answer 20

Let me check.

Answer 21

\[
(5)^2+(5)−9=25+5-9=21
\]Yes, that is right.

Answer 22

This question was a bit unfair because I still haven't give you all the limit properties yet.
However challenging questions are good.

Answer 23

So once you know what the limit is, it only takes an alg1 skill to solve it?

Answer 24

Here is another property of limits:
Suppose that \(f(x)=x\). Then: \[
\lim_{x\to a}x = a
\]

Answer 25

(I play chess online rating 2450)

Answer 26

Well, most limits can be solved with just algebra. There is one technique that requires derivatives. We'll get into that later.

Answer 27

I am patios

Answer 28

OK!

Answer 29

Hey Rachel!

Answer 30

Okay, so with the property I just showed you: \[
\lim_{x\to 100}x=L
\]What is \(L\)?

Answer 31

100

Answer 32

Okay good.

Answer 33

Oh studying! ...don't want to interrupt!

Answer 34

Here is another property of limits: \[
\lim_{x\to a}x^n=a^n
\]

Answer 35

a

Answer 36

it is limited to a

Answer 37

What is \(L\) for:\[
\lim_{x\to 4}x^3=L
\]

Answer 38

WOW!

Answer 39

1?

Answer 40

or cube root of 4

Answer 41

Nope. Remember:\[
\lim_{x\to a}x^n=a^n
\]
You need to identify \(a\) and \(n\).

Answer 42

rachel, thank you!

Answer 43

How?

Answer 44

\[
\lim_{x\to \color{blue} 4}x^{\color{red}3}=L
\]

Answer 45

\[
\lim_{x\to \color{blue}a}x^{\color{red}n}=\color{blue}a^{\color{red}n}
\]

Answer 46

I hope the color helps you see the pattern.

Answer 47

in your 1st equation, the exponent is 3 right?

Answer 48

Yes.

Answer 49

In your last question...

Answer 50

The last equation is a general formula.

Answer 51

I can cancel the n roots so I will have x be limited to a

and in the last, hold on need to think about that one for sec!

Answer 52

The first equation is a sample problem. You use the formula to solve it

Answer 53

the answer is 2 (for the 1st equation)

Answer 54

\[
\lim_{x\to \color{blue} 4}x^{\color{red}3}=\color{blue}4^{\color{red}3}=64
\]

Answer 55

My bad!

Answer 56

64?

Answer 57

By the way, cube root \(\sqrt[3]{4}\) is close but it is like the opposite answer..

Answer 58

the opposite?
multiplicative inverse?

Answer 59

I mean the idea was close, but it was still wrong because you did opposite of what you should do.

Answer 60

And what should I...?

Answer 61

\(\color{blue}{\text{Originally Posted by}}\) @wio
\[
\lim_{x\to \color{blue} 4}x^{\color{red}3}=\color{blue}4^{\color{red}3}=64
\]
\(\color{blue}{\text{End of Quote}}\)

Answer 62

This is the correct answer.

Answer 63

So you should do \(4^3\)

Answer 64

So you do everything to a third power

Answer 65

Yeah. Let us do one more problem with this property. \[
\lim_{x\to a}x^3 = 8
\]What is \(a\)?

Answer 66

2

Answer 67

Good.

Answer 68

TNX!

Answer 69

Different question, if you want more medals?

Answer 70

Alright.

Answer 71

(which you deserve!)