Thread: One more epsilon ?

I am given

f(x) = sq root x
Xo= 1
L=1
E= 1/4
y= sq root x

and it says

find a delta > 0 that for all x 0< abs value x-Xo < alpha -> abs value f(x)-L < E

I know on the right side I will have sq root x - 1 < 1/4

I am not sure what I put on the left side however. I know what Xo is but what about the x and the alpha?

I am so confused

Originally Posted by KarlosK

I am given

f(x) = sq root x
Xo= 1
L=1
E= 1/4
y= sq root x

and it says

find a delta > 0 that for all x 0< abs value x-Xo < alpha -> abs value f(x)-L < E

I know on the right side I will have sq root x - 1 < 1/4

I am not sure what I put on the left side however. I know what Xo is but what about the x and the alpha?

I am so confused

You want to find a δ>0 such that :

for all ,x : if o<|x-1|< δ ,then .................................................. ............................................1

But .................................................. ................................................2

Since

So from (2) we see that if we put |x-1|<1/4 ,then .

Obviously δ = 1/4