11. Find the equation of the tangent plane to the surface xyz + z²/3 = y² at (−1,1,1). 12. Use Green's Theorem to evaluate f xydx + x²dy on the path described by the boundary of the graphs y = x², y = √x oriented counterclockwise. 13. Evaluate the surface integral f f f (x, y, z)ds for f(x, y, z) = x²z², S: on the cone z² = x²+ y², between the planes z = 1, z=3. [Hint: converting to cylindrical/polar will help.]

Q: Select all that apply. Select the functions whose value is undefined. sec 90° cot 90° sin 270° cos…

A: NOTE: Refresh your page if you can't see any equations. .

Q: 1. Consider the surface defined by z = x2 + e9y ln(x-y). Let f(x,y) =  x2 + e9y ln(x-y). ○ Compute…

A: The given problem is to find the gradient vector of the given surface at point and to find the…

Q: Let f(x, y) = x² – y?. Find (b) The tangent plane to the surface given by f at the point (0, – 1).

A:

Q: 4. Find both points on the surface xz – x2 – y? = 8 where the tangent plane is horizontal.

A:

Q: Find the equation for the tangent plane to the surface z = 6x² - 8y² at the point (2, 1, 16). OA.…

A: NOTE: Refresh your page if you can't see any equations. . so the function f is, the given point…

Q: (a) The surface S is defined by x + y² + z³ = 3. Find a vector normal to S at the point A with…

A: For the multiple questions, we only provide the solution of first problem only as per our Q&A…

Q: 1. Find the equation of the tangent plane for the implicitly defined surface xy + xz+yz = 1

A: First we arrange the equation of the surface into the form  f(x,y,z)=0 xy+xz+yz-1=0