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.