Calculus Answers

A manufacturing process costs RM 6500 to set up for one year’s use. If items cost RM 85 each to produce and other costs amount to 3.5 x2, where x is the production in hundreds, find the level of production that will minimize the cost per item over the year. What will the total cost amount to at this level of production?

Apply separation of variable to solve

x²u_xy+9y²u=0

Solve the Cauchy Problem,

xu_x+(x+y)u_y=u+1 with u(x,y)=x² on y=0

Find the general solution of

(y-xu)p+(x+yu)q=x²+y²

Find the first partial derivative of

f(w, x, y, z) = w ^ 2 * x * y ^ 2 + x * y ^ 3 * z ^ 2

Find the first partial derivative of

h(x, y, z) = cos(x+y+z)

Find the first partial derivative of

s(y, z) = z ^ 2 * tan yz

I. Change the following point from polar to rectangular coordinate.

(3/2, n/12)

II. Evaluate f²(3ײ- 6x ‐2)dx

Find partial z partial x and partial z partial y for

z ^ 4 - y ^ 2 + x ^ 2 = 6x ^ 2 * y ^ 3 * z ^ 7 .