How do I solve this? | Mathematics | Page 1

vivid forge Oct 2, 2023, 5:36 AM

#

brave mistBOT Oct 2, 2023, 5:36 AM

#

unreal kettle Oct 2, 2023, 5:36 AM

#

l'hopital it i guess

vivid forge Oct 2, 2023, 5:51 AM

#

Could you try it?

#

I am getting it wrong somehow

unreal kettle Oct 2, 2023, 5:57 AM

#

sure gimme a min

#

yeah man you gotta appy the quotient rule the u/v rule

#

you'll get it

lime blaze Oct 2, 2023, 6:09 AM

#

Uh, there's no quotient rule if you apply L'Hopital's

#

Also, if OP hasn't seen L'H, then he's probably not allowed to use it.

frail sigil Oct 2, 2023, 7:06 AM

#

I'd try factoring it and see where I get. Or multiplying the whole expression with the root.

vivid forge Oct 2, 2023, 7:08 AM

#

This may be a very silly questions, but can you use derivatives to solve limits?

#

I.e, could I use the quotient rule here?

#

Also, could someone explain to me the L'H rule?

#

I am confused.

frail sigil Oct 2, 2023, 7:09 AM

#

Don't use it if you don't know it yet. Your school/college will propably tell you when you need it.

#

If you're insanely curious just google it.

vivid forge Oct 2, 2023, 7:09 AM

#

So, if you don't mind, could you try to solve this question?

#

Then send me your working?

#

I can't seem to get it

frail sigil Oct 2, 2023, 7:10 AM

#

I'll try.

vivid forge Oct 2, 2023, 7:10 AM

#

Thanks man

#

Appreciate it alot

lime blaze Oct 2, 2023, 7:12 AM

#

Do you know how to solve limits going to infinity in general? There's really only one method for rational functions, and that one method applies here.

#

For example, if the square root were not there, could you solve it?

vivid forge Oct 2, 2023, 7:13 AM

#

Yes, I can solve limits going to infinity in general.

#

The square root is what confuses me

lime blaze Oct 2, 2023, 7:13 AM

#

exact same method though

#

multiply numerator and denominator both by 1/x^2

frail sigil Oct 2, 2023, 7:15 AM

#

Ok I solved it in a more or equal way as O Dog.

#

Just start factoring the numerator and denominator with x^2 and cancel it.

vivid forge Oct 2, 2023, 7:16 AM

#

By why x^2?

#

I thought you do by the highest power

lime blaze Oct 2, 2023, 7:16 AM

#

So you know that the lower exponents don't matter, right?

#

Look at your denominator and ignore the terms of lower degree

#

what's left?

frail sigil Oct 2, 2023, 7:16 AM

#

yes you can do x^4 but x^2 twice also works and it looks "better"

vivid forge Oct 2, 2023, 7:17 AM

#

lime blaze what's left?

Is it just 9x^4

lime blaze Oct 2, 2023, 7:17 AM

#

vivid forge Is it just 9x^4

under a square root

vivid forge Oct 2, 2023, 7:18 AM

#

Yeah. Let me try the question again.

#

Hold on

#

What did you get @frail sigil

frail sigil Oct 2, 2023, 7:23 AM

#

You tell me!

vivid forge Oct 2, 2023, 7:23 AM

#

I got it wrong...

#

I somehow got 5/6x

frail sigil Oct 2, 2023, 7:24 AM

#

Actually you can cancel all the x's in the numerator and denominator and all you're left with are terms like 1/x that approach zero for x->infinity

#

So in the end you will get one fraction without x's

#

but the 5 in the numerator seems right!

#

@vivid forge do you want to send in your work?

vivid forge Oct 2, 2023, 7:26 AM

#

Yeah hold on.

#

#

What am I doing wrong?

lime blaze Oct 2, 2023, 7:31 AM

#

Consider $4 \sqrt{9} = \sqrt{4 \times 9}$?

analog orbitBOT Oct 2, 2023, 7:31 AM

#

O Dog

lime blaze Oct 2, 2023, 7:32 AM

#

You also shouldn't remove the fractions that are going to 0 until you actually resolve the limit, though that isn't going to cause a wrong answer here.

vivid forge Oct 2, 2023, 7:33 AM

#

lime blaze You also shouldn't remove the fractions that are going to 0 until you actually r...

Why is that?

vivid forge Oct 2, 2023, 7:33 AM

#

analog orbit **O Dog**

No, this is not the case.

lime blaze Oct 2, 2023, 7:34 AM

#

So when you multiply 1/x^2 into the denominator, you can't just put it in the square root

#

you need to rewrite it as a square root first

vivid forge Oct 2, 2023, 7:35 AM

#

What do you mean rewrite it as a square root?

lime blaze Oct 2, 2023, 7:35 AM

#

analog orbit **O Dog**

Can you fix this?

#

$4 \sqrt{9} = \sqrt{\textrm{what goes here?} \times 9}$

analog orbitBOT Oct 2, 2023, 7:36 AM

#

O Dog

vivid forge Oct 2, 2023, 7:38 AM

#

16?

lime blaze Oct 2, 2023, 7:38 AM

#

Right

#

$\frac{1}{x^2}\sqrt{y} = \sqrt{? \times y}$

analog orbitBOT Oct 2, 2023, 7:39 AM

#

O Dog

vivid forge Oct 2, 2023, 7:41 AM

#

(1/x^2)^2 x y

#

= 1/x^4 x Y ?

lime blaze Oct 2, 2023, 7:42 AM

#

I think you can do the whole thing now

vivid forge Oct 2, 2023, 7:42 AM

#

IS what I did right?

vivid forge Oct 2, 2023, 7:42 AM

#

vivid forge = 1/x^4 x Y ?

..

#

Okay, let me have a go!

#

Thanks man

frail sigil Oct 2, 2023, 7:56 AM

#

Do you have a solution now?

vivid forge Oct 2, 2023, 8:05 AM

#

YES!

#

Thank you so much for your help guys!

#

And your patience 🙂

frail sigil Oct 2, 2023, 8:08 AM

#

What is your solution though? Or did you check it online?

vivid forge Oct 2, 2023, 9:14 AM

#

Sorry for the late reply, just saw your message

#

My solution was 5/3

#

@frail sigil

frail sigil Oct 2, 2023, 9:18 AM

#

yes! I also had that 🙂

#

If you have no questions left mark as solved! @vivid forge

vivid forge Oct 2, 2023, 9:19 AM

#

Wait, I have one more sorry

#

Should be quick

#

#

How would I do f(51)?

#

@frail sigil

frail sigil Oct 2, 2023, 9:24 AM

#

Since we don't know what f(x) looks like when x is anything different than the first two cases I'd say the only thing you can write in that box is f(51)=f(59)

#

I don't know if it's right, but you could go backwards

vivid forge Oct 2, 2023, 9:25 AM

#

That's not right. I tried that

frail sigil Oct 2, 2023, 9:26 AM

#

So since f(x+8) is equal to f(x) we get f(51)=f(43 +8)=f(43)=f(35+8)=f(35)=f(27+8)=f(27)=f(19+8)=f(19)=f(11+8)=f(11)=f(3+8)=f(3)

#

and now you can calculate f(3)

vivid forge Oct 2, 2023, 9:27 AM

#

That's right!

#

Why though?

#

Why does that work? What's the logic?

frail sigil Oct 2, 2023, 9:27 AM

#

It's a periodic function!

vivid forge Oct 2, 2023, 9:27 AM

#

Don't understand.

#

Oh okay

frail sigil Oct 2, 2023, 9:27 AM

#

The third statement of the piecewise defined function tells us, that it repeats itself

vivid forge Oct 2, 2023, 9:27 AM

#

Why did you stop at 3 though?

frail sigil Oct 2, 2023, 9:27 AM

#

Because for 3 I can calculate it.

vivid forge Oct 2, 2023, 9:27 AM

#

Oh oaky.

#

okay

#

Thank you so much

frail sigil Oct 2, 2023, 9:28 AM

#

I hope it was kind of understandable

vivid forge Oct 2, 2023, 9:28 AM

#

It was!

frail sigil Oct 2, 2023, 9:28 AM

#

rin

#

@vivid forge write .solved if you have no questions left

vivid forge Oct 2, 2023, 9:37 AM

#

.solved

#How do I solve this?