Discussion about math, puzzles, games and fun. Useful symbols: ÷ × ½ √ ∞ ≠ ≤ ≥ ≈ ⇒ ± ∈ Δ θ ∴ ∑ ∫ π -¹ ² ³ °

You are not logged in.

- Topics: Active | Unanswered

**anonimnystefy****Real Member**- From: The Foundation
- Registered: 2011-05-23
- Posts: 15,507

hi gAr

what,no new limits?my brain will dumb out if i don't get my dose of math.

*Last edited by anonimnystefy (2011-07-02 00:07:31)*

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

Offline

**gAr****Member**- Registered: 2011-01-09
- Posts: 3,478

Hi anonimnystefy,

I find most of the limits yield to the techniques discussed here.

I'll post if I find something extraordinary!

"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."

Offline

**gAr****Member**- Registered: 2011-01-09
- Posts: 3,478

**12)**

**Warning!** Easy 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."

Offline

**anonimnystefy****Real Member**- From: The Foundation
- Registered: 2011-05-23
- Posts: 15,507

hi gAr

*Last edited by anonimnystefy (2011-07-02 03:40:04)*

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

Offline

**gAr****Member**- Registered: 2011-01-09
- Posts: 3,478

Hi anonimnystefy,

"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."

Offline

**reconsideryouranswer****Member**- Registered: 2011-05-11
- Posts: 172

**9)**

gAr wrote:

I couldn't come up with another method, can you?

Let x = 1/y. As x --> 0, then 1/y --> 0.

So y --> oo (or -oo).

The limit could be expressed as:

Notes:

--------

Step 2 to step 3 used the Binomial Theorem.

Step 3 through step 5 could use some

justification/details to support the

continued patterns of terms and expressions,

respectively.

*Last edited by reconsideryouranswer (2011-07-03 20:00:32)*

Signature line:

I wish a had a more interesting signature line.

Offline

**gAr****Member**- Registered: 2011-01-09
- Posts: 3,478

Hi reconsideryouranswer,

Thanks, good answer!

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

Offline

**anonimnystefy****Real Member**- From: The Foundation
- Registered: 2011-05-23
- Posts: 15,507

hi gAr

Would you don't mind if i post a problem?It's just that i don't want the topic to get forgotten.

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

Offline

**gAr****Member**- Registered: 2011-01-09
- Posts: 3,478

Hi anonimnystefy,

Absolutely!

Anyone may post limit questions here.

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

Offline

**anonimnystefy****Real Member**- From: The Foundation
- Registered: 2011-05-23
- Posts: 15,507

hi gAr

thanks.

here's one interesting limit:

i haven't encountered it yet and its kind hasn't been mentioned in this topic but it is one of the easier limits of this kind

*Last edited by anonimnystefy (2011-07-20 03:24:45)*

Here lies the reader who will never open this book. He is forever dead.

Offline

**gAr****Member**- Registered: 2011-01-09
- Posts: 3,478

Hi,

I too haven't done multivariable limits!

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

Offline

**anonimnystefy****Real Member**- From: The Foundation
- Registered: 2011-05-23
- Posts: 15,507

hi

here's another multivariable limit:

Here lies the reader who will never open this book. He is forever dead.

Offline

**anonimnystefy****Real Member**- From: The Foundation
- Registered: 2011-05-23
- Posts: 15,507

hi

these posts will be answered when i count to infinity and back.Maybe i should consult Chuck Norris.

Here lies the reader who will never open this book. He is forever dead.

Offline

**anonimnystefy****Real Member**- From: The Foundation
- Registered: 2011-05-23
- Posts: 15,507

just keeping the topic alive...

Here lies the reader who will never open this book. He is forever dead.

Offline

**bobbym****Administrator**- From: Bumpkinland
- Registered: 2009-04-12
- Posts: 85,215

Hi anonimnystefy;

Is this one you want help on?

I have never done one but I know how the packages do them. I think they nest the limits:

Just plug x = 0 into the limit:

**In mathematics, you don't understand things. You just get used to them.Of course that result can be rigorously obtained, but who cares?Combinatorics is Algebra and Algebra is Combinatorics.**

Offline

**anonimnystefy****Real Member**- From: The Foundation
- Registered: 2011-05-23
- Posts: 15,507

hi bobbym

that is one way that it can be done,but we can also do it

*Last edited by anonimnystefy (2011-07-22 23:59:42)*

Here lies the reader who will never open this book. He is forever dead.

Offline

**anonimnystefy****Real Member**- From: The Foundation
- Registered: 2011-05-23
- Posts: 15,507

you can do the second one as well.

Here lies the reader who will never open this book. He is forever dead.

Offline

**bobbym****Administrator**- From: Bumpkinland
- Registered: 2009-04-12
- Posts: 85,215

Hi;

**In mathematics, you don't understand things. You just get used to them.Of course that result can be rigorously obtained, but who cares?Combinatorics is Algebra and Algebra is Combinatorics.**

Offline

**anonimnystefy****Real Member**- From: The Foundation
- Registered: 2011-05-23
- Posts: 15,507

hi bobbym

i think that should be right(or left).

Here lies the reader who will never open this book. He is forever dead.

Offline

**bobbym****Administrator**- From: Bumpkinland
- Registered: 2009-04-12
- Posts: 85,215

Hi;

I am not following you, are you saying the limits do not exist?

**In mathematics, you don't understand things. You just get used to them.Of course that result can be rigorously obtained, but who cares?Combinatorics is Algebra and Algebra is Combinatorics.**

Offline

**anonimnystefy****Real Member**- From: The Foundation
- Registered: 2011-05-23
- Posts: 15,507

the first limit does not exist and the second one is correct but i tried to make a very bad joke.

Here lies the reader who will never open this book. He is forever dead.

Offline

**bobbym****Administrator**- From: Bumpkinland
- Registered: 2009-04-12
- Posts: 85,215

Hi;

Why do you think that

Does not exist?

Of course that result can be rigorously obtained, but who cares?

Combinatorics is Algebra and Algebra is Combinatorics.

Offline

**anonimnystefy****Real Member**- From: The Foundation
- Registered: 2011-05-23
- Posts: 15,507

i said that the second limit you did exists.that is the one you did in post #143.

Here lies the reader who will never open this book. He is forever dead.

Offline

**bobbym****Administrator**- From: Bumpkinland
- Registered: 2009-04-12
- Posts: 85,215

Hi;

Is it the one in #140?

Of course that result can be rigorously obtained, but who cares?

Combinatorics is Algebra and Algebra is Combinatorics.

Offline

**anonimnystefy****Real Member**- From: The Foundation
- Registered: 2011-05-23
- Posts: 15,507

the one in #140 doesn't exist because when we aproach it from two different paths it has different values.it is similair to the situation with one variable limits when the left and the right limit do not match up.

Here lies the reader who will never open this book. He is forever dead.

Offline