Basic Mathematics - Old Questions

1.(a) Define gradient of a vector function f(x, y, z) and find the derivative of

 f(x, y, z) = x³ - xy² - z at point P₀(1,1,0) in the direction of 𝑉⃗ = 2𝑖⃗ - 𝑗⃗ + 6𝑘⃗. [5]

(b) Define Volume of a solid and find the volume of the solid generated by revolving the region bounded by y = √x and the lines y = 1, x = 4 about the line y = 1. [5]