Question

Define g(x, y, z) = z2 sin(y − xz) + 2y. Answer the following questions. (a)...

Define g(x, y, z) = z2 sin(y − xz) + 2y. Answer the following questions.

(a) Compute the gradient of g at the point P = (1, 1, 1).

(b) The point P defined above is on the level surface g = C. What is the value of C?

(c) Find an equation of the tangent plane to the level surface g = C at the point P.

(d) Suppose we want to travel from the point P to the level surface g = C + 1. Estimate how far we have to go if we go in the direction that gets us there the fastest?

Math   Advanced-Math   
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
The tangent plane at (1,1,1) on the surface x2+y2+z2+xy+xz=5 is given by x+   y+ z=   (all values...
The tangent plane at (1,1,1) on the surface x2+y2+z2+xy+xz=5 is given by x+   y+ z=   (all values should be positive whole numbers with no common factors)
5.) a.) Integrate G(x,y,z)=xz over the sphere x2+y2+z2=9 b.) Integrate G(x,y,z)=x+y+z over the portion of the...
5.) a.) Integrate G(x,y,z)=xz over the sphere x2+y2+z2=9 b.) Integrate G(x,y,z)=x+y+z over the portion of the plane 2x+y+z=6 that lies in the first octant.
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.
Consider the function f(x, y) = sin(2x − 2y) (a) Solve and find the gradient of...
Consider the function f(x, y) = sin(2x − 2y) (a) Solve and find the gradient of the function. (b) Find the directional derivative of the function at the point P(π/2,π/6) in the direction of the vector v = <sqrt(3), −1>   (c) Compute the unit vector in the direction of the steepest ascent at A (π/2,π/2)
Suppose that X, Y, and Z are independent, with E[X]=E[Y]=E[Z]=2, and E[X2]=E[Y2]=E[Z2]=5. Find cov(XY,XZ). (Enter a...
Suppose that X, Y, and Z are independent, with E[X]=E[Y]=E[Z]=2, and E[X2]=E[Y2]=E[Z2]=5. Find cov(XY,XZ). (Enter a numerical answer.) cov(XY,XZ)= Let X be a standard normal random variable. Another random variable is determined as follows. We flip a fair coin (independent from X). In case of Heads, we let Y=X. In case of Tails, we let Y=−X. Is Y normal? Justify your answer. yes no not enough information to determine Compute Cov(X,Y). Cov(X,Y)= Are X and Y independent? yes no not...
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...
Please write down the details of reasons for your solutions. Thanks. Questions 2 a) Let f(x,y)...
Please write down the details of reasons for your solutions. Thanks. Questions 2 a) Let f(x,y) = sin (y^2 + e^(2x)). Find f(xy) and f(yx) and verify their equality. b) Find the equation of the tangent plane to the surface z=e^(2x)*cos(3y) at P (0, pi/3, -1) c) Find the direction in which the function f(x,y) = ((x-2y)/(2x+y))^(1/3) increases most rapidly at (1,0).
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
a) evaluate the directional derivative of z=F(x,y) = sin(xy) in the direction of u=(1,-1) at the...
a) evaluate the directional derivative of z=F(x,y) = sin(xy) in the direction of u=(1,-1) at the point (0,pi/2) b) Determine the slope of the tangent line c) State the tangent vector
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>.
ADVERTISEMENT
Need Online Homework Help?

Get Answers For Free
Most questions answered within 1 hours.

Ask a Question
ADVERTISEMENT