Questions from General Calculus

Q: Suppose you are climbing a hill whose shape is given by the

Suppose you are climbing a hill whose shape is given by the equation z = 1000 - 0.005x2 - 0.01y2, where x, y, and z are measured in meters, and you are standing at a point with coordinates (60, 40, 96...

Q: Shown is a topographic map of Blue River Pine Provincial Park in

Shown is a topographic map of Blue River Pine Provincial Park in British Columbia. Draw curves of steepest descent from point A (descending to Mud Lake) and from point B.

Q: Sketch the gradient vector ∆ f (4, 6) for

Sketch the gradient vector ∆ f (4, 6) for the function f whose level curves are shown. Explain how you chose the direction and length of this vector.

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. 2 (x – 2)2 + (y – 1)2 + (z – 3)2 = 10, (3, 3, 5)

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. x = y2 + z2 + 1, (3, 1, -1)

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. xy2z3 = 8, (2, 2, 1)

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. xy + yz + zx = 5, (1, 2, 1)

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. x + y + z = exyz, (0, 0, 1)

Q: Find the local maximum and minimum values and saddle point(s

Find the local maximum and minimum values and saddle point(s) of the function. If you have three-dimensional graphing software, graph the function with a domain and viewpoint that reveal all the impor...

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. x4 + y4 + z4 = 3x2y2z2, (1, 1, 1)