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## #1 2012-11-20 04:23:32

295Ja
Member
Registered: 2012-07-28
Posts: 39

### Limit

Hi! Please, help me with this one:

Evaluate the limit of (3-x)/(3-(sqrt of (6x-x²)) as x approaches 3 from the left.

What I did was this: I substitute 3 and found out that what I have is an indeterminate form of type 0/0. I then tried rationalizing the denominator but after it, I still arrived at the the same indeterminate form.

If what I did was right, please let me know the next step to solve the problem. If not, I'd like to ask for the right solution. I'll be waiting for replies then. Thanks in advance!

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## #2 2012-11-20 04:31:23

zetafunc.
Guest

### Re: Limit

Do you know L'Hopital's rule?

## #3 2012-11-20 04:41:08

295Ja
Member
Registered: 2012-07-28
Posts: 39

### Re: Limit

Not yet. We had just started studying limits. Do I need to learn that rule first to solve the problem I posted?

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## #4 2012-11-20 04:50:36

Mpmath
Member
Registered: 2012-10-11
Posts: 216

### Re: Limit

Hi;

L'Hopital's rule is the best way.

Winter is coming.

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## #5 2012-11-20 05:12:44

295Ja
Member
Registered: 2012-07-28
Posts: 39

### Re: Limit

Hi!
I tried to read about the L'Hopital's rule but I found out that for me to use that rule, I need to learn to evaluate derivatives.I must agree that the with the use of the rule, the solution would be simpler but may I ask for a solution  without using that rule? It is because we are not yet on derivatives and I think  the purpose of the problem, being included in the practice exercises of the topic that introduces limits, is for us to be able to master the basic theorems about limits that we had just learned.

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## #6 2012-11-20 06:16:08

anonimnystefy
Real Member
From: Harlan's World
Registered: 2011-05-23
Posts: 16,018

### Re: Limit

Hi 295Ja

No l'Hopital's rule needed.

Last edited by anonimnystefy (2012-11-20 06:16:48)

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.

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## #7 2012-11-20 10:18:37

295Ja
Member
Registered: 2012-07-28
Posts: 39

### Re: Limit

Hi stefy! Just want to say thanks!

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## #8 2012-11-20 19:27:18

anonimnystefy
Real Member
From: Harlan's World
Registered: 2011-05-23
Posts: 16,018

### Re: Limit

You're welcome!

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.

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