Consider the function\

z=f(x,y)=x^(2)+5xy^(3)

\ (a) Find

f(-2,-5)

.\

z=f(-2,-5)=

\ (b) Find a function

g(x,y,z)

whose level zero set is equal to the graph of

z=f(x,y)

and such that the coefficient of

z

in

g(x,y,z)

is 1 .\ The level set

g(x,y,z)=

\

=0 is the same as the graph of z=f(x,y).

\ (c) Find the gradient of

g

. Write your answer as a row vector of the general form

(:a,b,c:)

.\

gradg(x,y,z)=

\ (d) Use

gradg

to find a vector

vec(n)

perpendicular (or normal) to the graph of

z=f(x,y)

at the point

(-2,-5,1254)

. Write your answer as a row vector of the\ general form

(:a,b,c:)

.\

vec(n)=

\ (e) Find an equation for the tangent plane to

z=f(x,y)

at the point

(-2,-5,1254)

. Enter your answer as an equation.

Consider the function z=f(x,y)=x2+5xy3. (a) Find f(2,5). z=f(2,5)= (b) Find a function g(x,y,z) whose level zero set is equal to the graph of z=f(x,y) and such that the coefficient of z in g(x,y,z) is 1 . The level set g(x,y,z)= =0 is the same as the graph of z=f(x,y). (c) Find the gradient of g. Write your answer as a row vector of the general form a,b,c. g(x,y,z)= (d) Use g to find a vector n perpendicular (or normal) to the graph of z=f(x,y) at the point (2,5,1254). Write your answer as a row vector of th general form a,b,c. n= (e) Find an equation for the tangent plane to z=f(x,y) at the point (2,5,1254). Enter your answer as an equation