Questions from General Calculus

Q: Find the directional derivative of the function at the given point in

Find the directional derivative of the function at the given point in the direction of the vector v.

Q: Find the directional derivative of the function at the given point in

Find the directional derivative of the function at the given point in the direction of the vector v. f (x, y, z) = xy2 tan-1z, (2, 1, 1), v = 1, 1, 1

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. w = f (x, y, z), where x = x (u, v), y = y (u, v), z = z (u, v)

Q: Use the Chain Rule to find dz/dt or dw/

Use the Chain Rule to find dz/dt or dw/dt.

Q: If f (x, y) = xy, find the

If f (x, y) = xy, find the gradient vector =f (3, 2) and use it to find the tangent line to the level curve f (x, y) = 6 at the point (3, 2). Sketch the level curve, the tangent line, and the gradient...

Q: If t (x, y) = x2 + y2 -

If t (x, y) = x2 + y2 - 4x, find the gradient vector Vg = t (1, 2) and use it to find the tangent line to the level curve t (x, y) = 1 at the point (1, 2). Sketch the level curve, the tangent line, an...