Thread: Need 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...

You are looking for a value of such that whenever then .

Where do you get stuck?

Originally Posted by johnny4lsu

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...

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.

thanks a bunch. that way of doing it makes much more sense to me. Thanks again!