Questions from General Calculus

Q: Show that the equation of the tangent plane to the elliptic paraboloid

Show that the equation of the tangent plane to the elliptic paraboloid z/c = x2/a2 + y2/b2 at the point (x0, y0, z0) can be written as

Q: A function f is called homogeneous of degree n if it satisfies

A function f is called homogeneous of degree n if it satisfies the equation f (tx, ty) = tn f (x, y) for all t, where n is a positive integer and f has continuous second-order partial derivatives. (a)...

Q: If f is homogeneous of degree n, show that

If f is homogeneous of degree n, show that

Q: Show that every normal line to the sphere x2 + y2 +

Show that every normal line to the sphere x2 + y2 + z2 = r2 passes through the center of the sphere.

Q: Use a tree diagram to write out the Chain Rule for the

Use a tree diagram to write out the Chain Rule for the given case. Assume all functions are differentiable. T = F (p, q, r), where p = p (x, y, z), q = q (x, y, z), r = r (x, y, z)

Q: Suppose f is a differentiable function of x and y, and

Suppose f is a differentiable function of x and y, and t (r, s) = f (2r - s, s2 - 4r). Use the table of values in Exercise 15 to calculate tr (1, 2) and ts (1, 2). Exercise 15: Suppose f is a differ...

Q: Use a tree diagram to write out the Chain Rule for the

Use a tree diagram to write out the Chain Rule for the given case. Assume all functions are differentiable. R = F (t, u) where t = t (w, x, y, z), u – u (w, x, y, z)

Q: Use the Chain Rule to find the indicated partial derivatives.

Use the Chain Rule to find the indicated partial derivatives.

Q: Use the Chain Rule to find the indicated partial derivatives.

Use the Chain Rule to find the indicated partial derivatives.

Q: Use the Chain Rule to find the indicated partial derivatives.

Use the Chain Rule to find the indicated partial derivatives.