Math Is Fun Forum

bobbym

bumpkin

From: Bumpkinland

Registered: 2009-04-12

Posts: 109,606

Re: Limits!

Hi;

I got - ∞ for the one with the z in there. Thanks much for providing your solution.

---

In mathematics, you don't understand things. You just get used to them.
If it ain't broke, fix it until it is.
Always satisfy the Prime Directive of getting the right answer above all else.

gAr

Member

Registered: 2011-01-09

Posts: 3,482

Re: Limits!

Hi,

Okay.
You could've figured it out that there could be a mistake.
Thanks for telling!

---

"Believe nothing, no matter where you read it, or who said it, no matter if I have said it, unless it agrees with your own reason and your own common sense"  - Buddha?

"Data! Data! Data!" he cried impatiently. "I can't make bricks without clay."

anonimnystefy

Real Member

From: Harlan's World

Registered: 2011-05-23

Posts: 16,049

Re: Limits!

hi gAr

could you explain how you got the second line in your solution.i don't get it.

---

“Here lies the reader who will never open this book. He is forever dead.
“Taking a new step, uttering a new word, is what people fear most.” ― Fyodor Dostoyevsky, Crime and Punishment
The knowledge of some things as a function of age is a delta function.

gAr

Member

Registered: 2011-01-09

Posts: 3,482

Re: Limits!

Hi anonimnystefy,

I used L'Hospital's rule.

---

"Believe nothing, no matter where you read it, or who said it, no matter if I have said it, unless it agrees with your own reason and your own common sense"  - Buddha?

"Data! Data! Data!" he cried impatiently. "I can't make bricks without clay."

anonimnystefy

Real Member

From: Harlan's World

Registered: 2011-05-23

Posts: 16,049

Re: Limits!

aah.ok think i get it.

could you also make a topic on integrals?it would be nice to practice working on them.

Last edited by anonimnystefy (2011-06-30 01:05:20)

---

“Here lies the reader who will never open this book. He is forever dead.
“Taking a new step, uttering a new word, is what people fear most.” ― Fyodor Dostoyevsky, Crime and Punishment
The knowledge of some things as a function of age is a delta function.

bobbym

bumpkin

From: Bumpkinland

Registered: 2009-04-12

Posts: 109,606

Re: Limits!

Hi;

You can find a lot of them here.

http://www.mathisfunforum.com/viewtopic.php?id=4208

---

In mathematics, you don't understand things. You just get used to them.
If it ain't broke, fix it until it is.
Always satisfy the Prime Directive of getting the right answer above all else.

gAr

Member

Registered: 2011-01-09

Posts: 3,482

Re: Limits!

Hi bobbym,

I was searching for that url. Thanks!

---

"Believe nothing, no matter where you read it, or who said it, no matter if I have said it, unless it agrees with your own reason and your own common sense"  - Buddha?

"Data! Data! Data!" he cried impatiently. "I can't make bricks without clay."

bobbym

bumpkin

From: Bumpkinland

Registered: 2009-04-12

Posts: 109,606

Re: Limits!

Hi gAr;

I can not come up with anything better for #9 then using L'Hospitals rule.

---

In mathematics, you don't understand things. You just get used to them.
If it ain't broke, fix it until it is.
Always satisfy the Prime Directive of getting the right answer above all else.

gAr

Member

Registered: 2011-01-09

Posts: 3,482

Re: Limits!

Okay, no problem.
Thanks for looking into the problem.

---

"Believe nothing, no matter where you read it, or who said it, no matter if I have said it, unless it agrees with your own reason and your own common sense"  - Buddha?

"Data! Data! Data!" he cried impatiently. "I can't make bricks without clay."

bobbym

bumpkin

From: Bumpkinland

Registered: 2009-04-12

Posts: 109,606

Re: Limits!

Hi;

This works. Taylorize the numerator:

Now divide through by x and now it is easy to see what the limit is.

---

In mathematics, you don't understand things. You just get used to them.
If it ain't broke, fix it until it is.
Always satisfy the Prime Directive of getting the right answer above all else.

gAr

Member

Registered: 2011-01-09

Posts: 3,482

Re: Limits!

Hi bobbym,

Yes, I tried expanding like that.
But deriving that would require us to find limits anyway!

---

"Believe nothing, no matter where you read it, or who said it, no matter if I have said it, unless it agrees with your own reason and your own common sense"  - Buddha?

"Data! Data! Data!" he cried impatiently. "I can't make bricks without clay."

bobbym

bumpkin

From: Bumpkinland

Registered: 2009-04-12

Posts: 109,606

Re: Limits!

Hi;

Do you mean the derivatives, because the limits are done term by term?

Yes, you would have to find and prove the general term of that series ( done by induction ). Once you have the general term it is easy to see all terms after the constant term have an x in them and therefore zero out.

Oh wait, I see what you are saying! Good point. Even the f(0) could be a problem.

---

In mathematics, you don't understand things. You just get used to them.
If it ain't broke, fix it until it is.
Always satisfy the Prime Directive of getting the right answer above all else.

gAr

Member

Registered: 2011-01-09

Posts: 3,482

Re: Limits!

Hi,

Yes!
That's why I avoided giving that in my solution.

I thought maybe we can use binomial theorem, but that too fails. (or is it me?)

---

"Believe nothing, no matter where you read it, or who said it, no matter if I have said it, unless it agrees with your own reason and your own common sense"  - Buddha?

"Data! Data! Data!" he cried impatiently. "I can't make bricks without clay."

bobbym

bumpkin

From: Bumpkinland

Registered: 2009-04-12

Posts: 109,606

Re: Limits!

Hi gAr;

That is one way, maybe.

Also this is like a piece of experimental math. You use a package to get the answer and then you prove the answer is correct by induction. Sort of like the more classical use of guessing at the solution of a sum or a recurrence.

---

In mathematics, you don't understand things. You just get used to them.
If it ain't broke, fix it until it is.
Always satisfy the Prime Directive of getting the right answer above all else.

gAr

Member

Registered: 2011-01-09

Posts: 3,482

Re: Limits!

Hi bobbym,

Yes, I agree.

---

"Believe nothing, no matter where you read it, or who said it, no matter if I have said it, unless it agrees with your own reason and your own common sense"  - Buddha?

"Data! Data! Data!" he cried impatiently. "I can't make bricks without clay."

bobbym

bumpkin

From: Bumpkinland

Registered: 2009-04-12

Posts: 109,606

Re: Limits!

Hi;

In this case since proving the answer you get is going to be difficult at least from what I see, I think it is easier to use your way.

---

In mathematics, you don't understand things. You just get used to them.
If it ain't broke, fix it until it is.
Always satisfy the Prime Directive of getting the right answer above all else.

gAr

Member

Registered: 2011-01-09

Posts: 3,482

Re: Limits!

Hi bobbym,

I think so. From what I know, no other tricks I can think of.

---

"Believe nothing, no matter where you read it, or who said it, no matter if I have said it, unless it agrees with your own reason and your own common sense"  - Buddha?

"Data! Data! Data!" he cried impatiently. "I can't make bricks without clay."

anonimnystefy

Real Member

From: Harlan's World

Registered: 2011-05-23

Posts: 16,049

Re: Limits!

hi gAr

how about a hint on the 10?

---

“Here lies the reader who will never open this book. He is forever dead.
“Taking a new step, uttering a new word, is what people fear most.” ― Fyodor Dostoyevsky, Crime and Punishment
The knowledge of some things as a function of age is a delta function.

gAr

Member

Registered: 2011-01-09

Posts: 3,482

Re: Limits!

Hi anonimnystefy,

It's already solved in #94.

---

"Believe nothing, no matter where you read it, or who said it, no matter if I have said it, unless it agrees with your own reason and your own common sense"  - Buddha?

"Data! Data! Data!" he cried impatiently. "I can't make bricks without clay."

123ronnie321

Member

Registered: 2010-09-28

Posts: 128

Re: Limits!

I hope my steps are correct.

anonimnystefy

Real Member

From: Harlan's World

Registered: 2011-05-23

Posts: 16,049

Re: Limits!

hi 123ronnie123

how did you get the next to last line?

---

“Here lies the reader who will never open this book. He is forever dead.
“Taking a new step, uttering a new word, is what people fear most.” ― Fyodor Dostoyevsky, Crime and Punishment
The knowledge of some things as a function of age is a delta function.

123ronnie321

Member

Registered: 2010-09-28

Posts: 128

Re: Limits!

Hi anonimnystefy,
I am unsure about the ending of my solution and I am waiting for either gAr's or Bobbym's help.

gAr

Member

Registered: 2011-01-09

Posts: 3,482

Re: Limits!

Hi 123ronnie321,

---

"Believe nothing, no matter where you read it, or who said it, no matter if I have said it, unless it agrees with your own reason and your own common sense"  - Buddha?

"Data! Data! Data!" he cried impatiently. "I can't make bricks without clay."

123ronnie321

Member

Registered: 2010-09-28

Posts: 128

Re: Limits!

Thanks for your help, gAr.

gAr

Member

Registered: 2011-01-09

Posts: 3,482

Re: Limits!

Hi,

You're welcome!

---

"Believe nothing, no matter where you read it, or who said it, no matter if I have said it, unless it agrees with your own reason and your own common sense"  - Buddha?

"Data! Data! Data!" he cried impatiently. "I can't make bricks without clay."