Question

Given the level surface S defined by f(x, y, z) = x − y3 − 2z2...

Given the level surface S defined by f(x, y, z) = x − y3 − 2z2 = 2 and the point P0(−4, −2, 1).

Find the equation of the tangent plane to the surface S at the point P0.

Find the derivative of f at P0in the direction of r(t) =< 3, 6, −2 >

Find the direction and the value of the maximum rate of change greatest increase of f at P0;

(d) Find the parametric equations of the tangent line at P0 to the curve of intersection of S and 2x − 3y − z = -3.

Math   Calculus   
0 0
Add a commentTranscribed image text
Next >

Homework Answers

Answer #1

0 0
Know the answer?
Your Answer:

Post as a guest

Your Name:

What's your source?

Earn Coins

Coins can be redeemed for fabulous gifts.

Log In

Sign Up

Not the answer you're looking for?
Ask your own homework help question
Similar Questions
Consider the function F(x, y, z) =x2/2− y3/3 + z6/6 − 1. (a) Find the gradient...
Consider the function F(x, y, z) =x2/2− y3/3 + z6/6 − 1. (a) Find the gradient vector ∇F. (b) Find a scalar equation and a vector parametric form for the tangent plane to the surface F(x, y, z) = 0 at the point (1, −1, 1). (c) Let x = s + t, y = st and z = et^2 . Use the multivariable chain rule to find ∂F/∂s . Write your answer in terms of s and t.
Consider the surface S in R3 defined implicitly by x**2 y = 4ze**(x+y) − 35 ....
Consider the surface S in R3 defined implicitly by x**2 y = 4ze**(x+y) − 35 . (a) Find the equations of the implicit partial derivatives ∂z ∂x and ∂z ∂y in terms of x, y, z. (b) Find equations of the tangent plane and the norma line to the surface S at the point (3, −3, 2)
for the surface f(x/y/z)=x3+3x2y2+y3+4xy-z2=0 find any vector that is normal to the surface at the point...
for the surface f(x/y/z)=x3+3x2y2+y3+4xy-z2=0 find any vector that is normal to the surface at the point Q(1,1,3). use this to find the equation of the tangent plane to the surface at q.
16. a. Find the directional derivative of f (x, y) = xy at P0 = (1,...
16. a. Find the directional derivative of f (x, y) = xy at P0 = (1, 2) in the direction of v = 〈3, 4〉. b. Find the equation of the tangent plane to the level surface xy2 + y3z4 = 2 at the point (1, 1, 1). c. Determine all critical points of the function f(x,y)=y3 +3x2y−6x2 −6y2 +2.
We are given a level surface F ( x , y , z ) = 0...
We are given a level surface F ( x , y , z ) = 0 where F ( x , y , z ) = x^3 - y^2 + z^4 - 20 . Find the equation of the tangent plane to the surface at the point P ( 2 , 2 , 2 ) . Write the final answer in the form a x + b y + c z + d = 0
An implicitly defined function of x, y and z is given along with a point P...
An implicitly defined function of x, y and z is given along with a point P that lies on the surface: sin(xy) + cos(yz) = 0, at P = (2, π/12, 4) Use the gradient ∇F to: (a) find the equation of the normal line to the surface at P. (b) find the equation of the plane tangent to the surface at P.
Compute the surface integral of F(x, y, z) = (y,z,x) over the surface S, where S...
Compute the surface integral of F(x, y, z) = (y,z,x) over the surface S, where S is the portion of the cone x = sqrt(y^2+z^2) (orientation is in the negative x direction) between the planes x = 0, x = 5, and above the xy-plane. PLEASE EXPLAIN
Consider the surface defined by z = f(x,y) = x+y^2+1. a）Sketch axes that cover the region...
Consider the surface defined by z = f(x,y) = x+y^2+1. a）Sketch axes that cover the region -2<=x<=2 and -2<=y<=2.On the axes , draw and clearly label the contours for the eights z=0 ,z=1,and z=2. b)evaluate the gradients of f(x,y) at the point (x,y) = (0.-1), and draw the gradient vector on the contour diagrqam . c)compute the directional derivative at(x,y) = (0,-1) in the direction V =<2,1>.
(a) Find an equation of the plane tangent to the surface xy ln x − y^2...
(a) Find an equation of the plane tangent to the surface xy ln x − y^2 + z^2 + 5 = 0 at the point (1, −3, 2) (b) Find the directional derivative of f(x, y, z) = xy ln x − y^2 + z^2 + 5 at the point (1, −3, 2) in the direction of the vector < 1, 0, −1 >. (Hint: Use the results of partial derivatives from part(a))
Given S is the surface of the paraboloid z= 4-x^2-y^2 and C is the curve of...
Given S is the surface of the paraboloid z= 4-x^2-y^2 and C is the curve of intersection of the paraboloid with the plane z=0. Verify stokes theorem for the field F=2zi+xj+y^2k.( you might verify it by checking both sides of the theorem)
ADVERTISEMENT
Need Online Homework Help?

Get Answers For Free
Most questions answered within 1 hours.

Ask a Question
ADVERTISEMENT