Problem:

let f(x)=sqrt(19-x) and lim x-->10 f(x)=3 . Use the graph (or table) to find a value delta whenever epsilon=.5

Can someone please help me with this problem? Thanks

I don't even know where to begin...

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- June 21st 2009, 03:58 PMjohnny4lsuNeed help finding delta....
Problem:

let f(x)=sqrt(19-x) and lim x-->10 f(x)=3 . Use the graph (or table) to find a value delta whenever epsilon=.5

Can someone please help me with this problem? Thanks

I don't even know where to begin... - June 21st 2009, 04:33 PMBruno J.
You are looking for a value of such that whenever then .

Where do you get stuck? - June 21st 2009, 04:38 PMVonNemo19

This is how I do this

But, your problem says to find the value by lookind at the graph, which is much easier. I'll talk about that in a minute.

We wish to find an such that whenever

So here we just solve the double inequality

squaring (note that the direction of the signs is preserved)

So now we need to look at

So we choose

Analyling limits graphically, although imprecise, is easy.

1.Graph the function

2. graph the lines y=3, y=3.5, and y=2.5

3. where the lines y=3.5 and y=2.5 intersect the graph of the function, draw vertical lines.

x=10 will be in the interval where these lines cross. Approximate delta by choosing delta just a little bit smaller than the absolute value of the difference between 10 and the aproximate value of x where the vertical line closest to x=10 crosses the x-axis. this is your delta. - June 21st 2009, 05:00 PMjohnny4lsu
thanks a bunch. that way of doing it makes much more sense to me. Thanks again!