Calculus Answers

A rectangular gutter is formed by bending a 24 cm wide sheet of metal as shown. As a whole number, what is the height of a the gutter of maximum capacity?

Find equivalent functional definition for each of the following and draw a graph of the function.

f(x) = |x|•|x-1|

Find the equivalent functional definition for each of the following and draw a graph of the function.

f(x)= x+|x|.

Find equivalent functional definition for each of the following and draw a graph of a function.

f(x)=2x -|x| + |x-1|

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.