Show the limit in a derivative.  TOPIC_SOLVED

Limits, differentiation, related rates, integration, trig integrals, etc.

Show the limit in a derivative.

Postby GreenLantern on Mon Feb 28, 2011 5:00 pm

Problem: Use the definition of f'(x) in terms to show that the derivative of is

My understanding is that I'm supposed to use the notion of the change in f(x) (also known as f'(x), correct?) to show a limit. As far as I'm concerned though, f(x) is just a parabola and doesn't ever experience the "limit" aspect anywhere so defining f'(x) as a limit seems a little silly.
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Re: Show the limit in a derivative.

Postby Martingale on Mon Feb 28, 2011 8:30 pm

GreenLantern wrote:Problem: Use the definition of f'(x) in terms to show that the derivative of is

My understanding is that I'm supposed to use the notion of the change in f(x) (also known as f'(x), correct?) to show a limit. As far as I'm concerned though, f(x) is just a parabola and doesn't ever experience the "limit" aspect anywhere so defining f'(x) as a limit seems a little silly.



you are supposed to show that




for
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Re: Show the limit in a derivative.

Postby GreenLantern on Wed Mar 02, 2011 2:45 pm

Okay, so I'm still trying to wrap my head around this one, but I think I understand enough to make another post.

What we have normally dealt with is a limit being super super simple, like

To show that Y never actually is 1, but is always getting closer to it.

Now, the problem is asking me to show how Y is always approaching 6x-1 but never actually is.

Alright... I can do that.
So I start with my original function.


Now I make a little chart to show values to compare them.
When x=1


When x=10


But now I am immediately confused, because while this is normally how we showed that this was where the function never crossed we can see that it clearly does. Meaning that there is a point where f(x)=f'(x) and it's between 1&10 (I didn't take the time to find the exact point). How is this a "limit" if it does in fact cross over?

I'm not really sure where the

is coming from. I'm assuming that's the general equation for a derivative?
So do I just plug all that in and solve for 6x-1?
What is h supposed to equal? 6x-1?

I don't have time at the moment, but I'll be back in an hour and solve this one...
Last edited by GreenLantern on Wed Mar 02, 2011 2:54 pm, edited 1 time in total.
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Re: Show the limit in a derivative.  TOPIC_SOLVED

Postby Martingale on Wed Mar 02, 2011 2:54 pm

GreenLantern wrote:Okay, so I'm still trying to wrap my head around this one, but I think I understand enough to make another post.

What we have normally dealt with is a limit being super super simple, like

To show that Y never actually is 1, but is always getting closer to it.

Now, the problem is asking me to show how Y is always approaching 6x-1 but never actually is.

Alright... I can do that.
So I start with my original function.


Now I make a little chart to show values to compare them.
When x=1


When x=10


But now I am immediately confused, because while this is normally how we showed that this was where the function never crossed we can see that it clearly does. Meaning that there is a point where f(x)=f'(x) and it's between 1&10 (I didn't take the time to find the exact point). How is this a "limit" if it does in fact cross over?



I have No idea what you are doing....

your original question asked for you to show that ...



using the definition of a derivative

ie

show that



you might want to consult your book to remind yourself what a limit really is and what the definition of a derivative is.
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Re: Show the limit in a derivative.

Postby GreenLantern on Wed Mar 02, 2011 2:56 pm

Whoa, okay. Fast posting. I did a little editing...

I'll be back, I have class. See if I can't get this all straightened out... Ya, I hit my book again before I come back though.
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