I need to show that P<->Q is logically equivalent to ( P ^ Q ) v ( ~P ^ ~Q)
So far I have P <-> Q is equivalent to ( ~P v Q ) ^ ( ~Q v P ) by a example
I have no idea where to go from here
1.I can't figure out how the \sqrt{1+((x^2)/(4-x^2))} simplifies to 2 times\sqrt{1/(4-x^2)}
I have tried rewriting it in different ways, but I can't see how it simplifies. \sqrt{x^2 + 1/4-x^2}
1. I am suppose to find the surface area of the curve y=sqrt(4-x^2) from -1 to 1 when it is revolving around the x-axis.
2. Homework Equations : S= 2PIf(x)sqrt(1+(dy/dx)^2)dx
3. I found the derivative to be -x(4-x^2)^-1/2 and then squared it so the problem is 2Pi -1\int1...
Surface area by revolving a curve problem, help!
can someone show me how to solve for the surface area when rotating y=sqrt(4-x^2) around the x-axis from -1 < x < 1.
shows the steps please!
thanks