l-hospital's rule

Maiya · 2011-09-05 23:42:21

how is the usage of this to be done?????????
can anyone help me with that..............??

bobbym · 2011-09-05 23:48:33

Hi Maiya;

Welcome! I think you need to be a little bit more specific.

zetafunc. · 2011-09-06 05:13:13

It's used to try to evaluate limits that give you an undefined answer or the indeterminate form (0/0) for a function. Example:

evaluate

L'Hopital's rule says we take the derivative of the top and bottom, since substituting x = 0 just gives us an indeterminate form.

In general;

However, this only works if both f(x) and g(x) approach 0 or it diverges (approaches positive or negative infinity). After using L'Hopital's rule, it is also a requirement that

exists, too.

Maiya · 2011-09-07 00:08:32

thank you but limits are applied when a function is indeterminate right?????

bobbym · 2011-09-07 00:10:09

Hi Maiya;

L' Hopitals rule is applied when a limit is indeterminate.

Maiya · 2011-09-07 00:34:34

then limits are applied because..............???

Maiya · 2011-09-07 00:36:41

i mean what for are they applied

bobbym · 2011-09-07 00:39:51

Hi;

Take a look here:

http://www.coolmath.com/lesson-whats-a-limit-1.htm

Maiya · 2011-09-07 00:50:44

but how can the functions be equal to their derivatives
?????

anonimnystefy · 2011-09-07 00:52:42

hi Maiya

they are not equal equal,but their limits,when undefined,are equal.

Maiya · 2011-09-07 00:53:42

so they are just asumed to be equal

bobbym · 2011-09-07 00:58:00

Who said they are equal to their derivatives?

Which are you asking about limits or derivatives?

but how can the functions be equal to their derivatives

The exponential function is equal to its derivative.

Did you read the page I sent you too?

Maiya · 2011-09-07 23:44:31

Hello bobbym;
i want to know about l-hospital's rule
yes i did read that pages u sent
they were a great help
thank u for making me recall limits

bobbym · 2011-09-07 23:46:30

Hi;

L' Hopitals rule is for evaluating limits of the form ∞ / ∞ and few others. That is all there is to what it is.

Maiya · 2011-09-08 00:07:34

what do u guys do any way
how come u all know that much about these things???????

bobbym · 2011-09-08 00:09:23

I was just asked that same question.

She: Do you know everything!

Me: I don't know...

Maiya · 2011-09-08 00:11:57

I didn't ask u do u know everything
i just asked u what do u guys do................

bobbym · 2011-09-08 00:13:53

See my signature, the one on the very bottom? That is it in a nutshell for me. I do not know about everyone else.

Maiya · 2011-09-08 00:29:22

Its great how u guys know everything...............

bobbym · 2011-09-08 00:37:07

No one knows everything.

Would you like to see L' Hopitals rule actually do something useful?

Maiya · 2011-09-08 00:40:49

ya

bobbym · 2011-09-08 00:42:06

It will be a little lengthy so please hold on.

Maiya · 2011-09-08 00:43:20

Isn't using LaTeX a bit too hard .................

bobbym · 2011-09-08 00:44:29

Nope! You get used to it. There are many good tutorials and good programs to help. I use an online program that does it for you.

bobbym · 2011-09-08 00:56:39

Here is a real world example. You are asked to graph the function:

From 0 to 1. So you enter your x values into a calculator to get your x y table. You put in sin(0) / 0 and your calculator explodes! So what do you do with the point x = 0?

Now the math types will just go crazy with what I am going to say so I hope none of em are around.

Here is what we do:

We see that this limit is of the form 0 / 0 so we can use L' Hopitals rule on it.

Now we have a much simpler limit.

So for x = 0 we would put y = 1 in the chart. Now to those math types that is a sacrilege. They will point out that that is not the value of sin(x)/x at x = 0. They will say that the limit just means it approaches one. That we can make the answer as close to 1 as we need it to be.

True! But when working with computers we need numbers not concepts! The above process is done in numerical integration, curve fitting and plotting.

Math Is Fun Forum

#1 2011-09-05 23:42:21

l-hospital's rule

#2 2011-09-05 23:48:33

Re: l-hospital's rule

#3 2011-09-06 05:13:13

Re: l-hospital's rule

#4 2011-09-07 00:08:32

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#5 2011-09-07 00:10:09

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#6 2011-09-07 00:34:34

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#7 2011-09-07 00:36:41

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#8 2011-09-07 00:39:51

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#9 2011-09-07 00:50:44

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