Questions from General Calculus

Q: Find equations of (a) the tangent plane and (b

Find equations of (a) the tangent plane and (b) the normal line to the given surface at the specified point. sin (xyz) = x + 2y + 3z, (2, 21, 0)

Q: Use a computer to graph the surface z = x2 + y4

Use a computer to graph the surface z = x2 + y4 and its tangent plane and normal line at (1, 1, 2) on the same screen. Choose the domain and viewpoint so that you get a good view of all three objects....

Q: Find the points on the hyperboloid x2 + 4y2 - z2 =

Find the points on the hyperboloid x2 + 4y2 - z2 = 4 where the tangent plane is parallel to the plane 2x + 2y + z = 5.

Q: Calculate the value of the multiple integral. ∭E z

Calculate the value of the multiple integral. ∭E z dV, where E is bounded by the planes y = 0, z = 0, x + y = 2 and the cylinder y2 + z2 = 1 in the first octant.

Q: Calculate the value of the multiple integral. ∭E yz

Calculate the value of the multiple integral. ∭E yz dV, where E lies above the plane z = 0, below the plane z = y, and inside the cylinder x2 + y2 = 4

Q: The two legs of a right triangle are measured as 5 m

The two legs of a right triangle are measured as 5 m and 12 m with a possible error in measurement of at most 0.2 cm in each. Use differentials to estimate the maximum error in the calculated value of...

Q: Find the minimum value of f (x, y, z

Find the minimum value of f (x, y, z) = x2 + 2y2 + 3z2 subject to the constraint x + 2y + 3z = 10. Show that f has no maximum value with this constraint.

Q: Find the volume of the given solid. Under the paraboloid

Find the volume of the given solid. Under the paraboloid z = x2 + 4y2 and above the rectangle R = [0, 2] × [1, 4]

Q: Find the volume of the given solid. Under the surface

Find the volume of the given solid. Under the surface z = x2y and above the triangle in the xy-plane with vertices (1, 0), (2, 1), and (4, 0)

Q: Find the volume of the given solid. The solid tetrahedron

Find the volume of the given solid. The solid tetrahedron with vertices (0, 0, 0), (0, 0, 1), (0, 2, 0), and (2, 2, 0)