a) Determine the gradient of

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

at

(3,2,1)

.\ b) Consider the surface\

f(x,y,z)=(3x^(4))/(\\\\sqrt(y^(3)))-z\\\\sqrt(y^(3))+5x^(2)\\\\sqrt(z)=0

\ for

x,y,&z

all

>0

. Determine the component of a vector normal to this\ surface at

(0,1,2)

in the direction of the vector

vec(A)=hat()+2widehat(k)

.

a) Determine the gradient of f(x,y,x)=ln(x2+y2+2z3) at (3,2,1). b) Consider the surface f(x,y,z)=y33x4zy3+5x2z=0 for x,y,&z all >0. Determine the component of a vector normal to this surface at (0,1,2) in the direction of the vector A=^+2k. a) Determine the gradient of f(x,y,x)=ln(x2+y2+2z3) at (3,2,1). b) Consider the surface f(x,y,z)=y33x4zy3+5x2z=0 for x,y,&z all >0. Determine the component of a vector normal to this surface at (0,1,2) in the direction of the vector A=^+2k