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#1 2012-11-21 03:23:32

295Ja
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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!

#2 2012-11-21 03:31:23

zetafunc.
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Re: Limit

Do you know L'Hopital's rule?

#3 2012-11-21 03:41:08

295Ja
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Re: Limit

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

#4 2012-11-21 03:50:36

Mpmath
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Re: Limit

Hi;

L'Hopital's rule is the best way.


Winter is coming.

#5 2012-11-21 04:12:44

295Ja
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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.

#6 2012-11-21 05:16:08

anonimnystefy
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Re: Limit

Hi 295Ja



No l'Hopital's rule needed.

Last edited by anonimnystefy (2012-11-21 05:16:48)


The limit operator is just an excuse for doing something you know you can't.
“It's the subject that nobody knows anything about that we can all talk about!” ― Richard Feynman
“Taking a new step, uttering a new word, is what people fear most.” ― Fyodor Dostoyevsky, Crime and Punishment

#7 2012-11-21 09:18:37

295Ja
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Re: Limit

Hi stefy! Just want to say thanks! smile

#8 2012-11-21 18:27:18

anonimnystefy
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Re: Limit

You're welcome!


The limit operator is just an excuse for doing something you know you can't.
“It's the subject that nobody knows anything about that we can all talk about!” ― Richard Feynman
“Taking a new step, uttering a new word, is what people fear most.” ― Fyodor Dostoyevsky, Crime and Punishment

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