Calculus Answers

If F(u,v) = u-v/u+v, find F (1/u,1/v) + F (u,v).

y= log (1-2x)

If g(y) = y/(1-y), show that 1/2[g(y) + g(-y)]= g(y^2).

If f(x)= x(x+1), show that f(x +h)- f(x) = h(2x+1+h).

Identify the surface of the z² = 4 + 4r² by converting them into equations in the Cartesian form. Show the complete solutions.

find the centroid of the region with the indicated boundaries y = 4 - x^2 and the x-axis

find the length of the arc of the curve 9y²= (x²+2)³ from the point where x=0 To the point where x = 2.

If f(x,y) = x^3 + 4xy^2 + y^3, show that f(ax, ay)= a^3 f(x,y).

If f(x) =10^x and Φ(x) =log10 x, show that f[Φ(x)] = Φ [f(x)] = x.

If f(x)= x^2 -1 and g (x) =2x +1, show that f[g(x)]=4x(x+1).