y,z) = 2x^2 + 2y^2 + 4z^2 - 8z,   find all points on f(x, y, z) = 16 where the tangent plane is perpendicular to the line given by

Q: Find the tangent plane to the equation z = z = 3x² + y² + 4y at the point (1, 0, 3)

A:

Q: Find an equation of the line tangent to the intersection of the cylinders x² + z² = 4, y² + z² = 4…

A: The parametric form of the tangent line is  x=x0+aty=y0+btz=z0+ct where, (a,b,c) is the direction…

Q: F(X, y,z) = 2x -y? +z?

A: F(x,y,z)= 2x-y^2-z^2 at point (4,-4,2) df/dx= 2 df/dy=-2y df/dz= -2z

Q: y - 2)2 + (x-2)2 . Find the direction of heat flow in the plate at the point (2, 1). Heat flows in…

A: Introduction: The gradient of the temperature function at the point is the direction of the greatest…

Q: G(x,y)= (x+3y) / (x^2 - y^2 ) Sketch the domain

A: G(x,y) = x + 3yx2 - y2 The denominator cannot be zero. Therefore, x2 - y2 ≠ 0(x+y)(x-y) ≠ 0x ≠ -yx ≠…

Q: For the function f(x,y)=x^3−2x^2y−y^2−y, which vector is normal to the level curve at the point…

A:

Q: An object is traveling along the line y = 2x + 1 heading up and to the right. If the temperature at…

A:

Q: SF. dr, where F (x, y) = (6x − 2y)i +x²7, Evaluate from (6,-3) to (0, 0). and C is the line segment

A:

Q: Find an equation of the tangent plane to the graph of F(r, s) at t F(r. s). - (3r4 1 + 1), (-1, 1.…

A: Introduction: Let z=f(x,y) denote the equation of a surface S in R3, and P=(a,b,c) denotes a point…

Q: A circular disk of radius 5 meters centered at the origin has been unevenly heated. The temperature…

A: To find where the temperature on the disk is the greatest, we need to find the maximum value of the…

Q: Compute F · dr where F(x, y) = and C is the path traced by the line segment starting at (0, −1) and…

A:

Q: The temperature at the point (x, y) on a metal plate is given by T (x, y) = y/(x2 + y2 ). Find the…

A:

Q: (d) Find the directional derivative of f at (-2,1), in the direction of (-3,5).

A: Given f(x,y)=9-x2-y2 fx= -2x fy=-2y ∇f(x,y)=<fx,fy>=<-2x,-2y>…

Q: Find the unit vectors that are parallel to the tangent of the polynomial y= x^3 +2x + 1 at the point…

A: Consider the given function and differentiate to get the slope of the tangent.

Q: Find the indicated value for f(x,y) = x^2y^3  fxx(1,2) =  fyy(1,2) =  fxy(1,2) =  really…

A: Given query is to find indicated partial derivative.