Answer to Question #59579 in Calculus for RITA

Question

1 If ϕ=2xz4−x2y, find |▽ϕ|
(a) √(93)
(b) √(80)
(c) √(12)
(d) √(110)

2 If ϕ(x,y,z)=3x^2y−y^3z^2, find ▽ϕ at point (1,-2,-1)
(a) −12i−9j−16k
(b) i−3j−k
(c) 2i−5j−6k
(d) −3i−4j−2k

3 Find a unit normal to the surface x^2y+2xz=4 at point (2,-2,3)
(a) 2/3i−2/3j−2/3k
(b) −1/5i+2/5j+2/5k
(c) −1/3i+2/3j+2/3k
(d) −1/7i+2/7j+2/7k

4 Let ϕ(x,y,z)=xy^2z and A=xzi−xy^2j+yz^2k,find ∂^3/∂x^2∂z(ϕA)
(a) 2i+2j−5k
(b) 5i−k
(c) 4i−2j
(c) i+j

5 Given that ϕ=2x^2y−xz^3 find ▽^2ϕ
(a) 2y−6xz
(b) 4y−6xz
(c) 2y−xz
(d) y+6xz