1)lim x goes 1 sgrt(3-2sin(pix/2)=1 prove that epsilon delta.
2)lim x goes pi/4 (sinx+cosx)=sgrt(2) prove that epsilon delta
3)lim x goes3 ((x^2)-9)[[3x]]=0 prove that epsilon delta.
You should know that if then .
So in this case, you need to show , or if you like, to show
This particular proof requires some knowledge of the Mean Value Theorem, in other words, that for some
Here our and , so by the Mean Value Theorem
Therefore we should choose .