Problem 1E Problem 2E: How do you compute the gradient of the functions f(x, y) and f (x, y, z)? Problem 3E Problem 4E Problem 5E: Given a function f, explain the relationship between the gradient and the level curves of f. Problem 6E: The level curves of the surface z=x2+y2 are circles in the xy-plane centered at the origin. Without... Problem 7E: Directional derivatives Consider the function f(x.y) = 8x2/2 y2. whose graph is a paraboloid (see... Problem 8E: Directional derivatives Consider the function f(x,y)=2x2+y2, whose graph is a paraboloid (see... Problem 9E: Computing gradients Compute the gradient of the following functions and evaluate it at the given... Problem 10E: Computing gradients Compute the gradient of the following functions and evaluate it at the given... Problem 11E: Computing gradients Compute the gradient of the following functions and evaluate it at the given... Problem 12E: Computing gradients Compute the gradient of the following functions and evaluate it at the given... Problem 13E: Computing gradients Compute the gradient of the following functions and evaluate it at the given... Problem 14E: Computing gradients Compute the gradient of the following functions and evaluate it at the given... Problem 15E: Computing gradients Compute the gradient of the following functions and evaluate it at the given... Problem 16E: Computing gradients Compute the gradient of the following functions and evaluate it at the given... Problem 17E: Computing directional derivatives with the gradient Compute the directional derivative of the... Problem 18E: Computing directional derivatives with the gradient Compute the directional derivative of the... Problem 19E Problem 20E: Computing directional derivatives with the gradient Compute the directional derivative of the... Problem 21E: Computing directional derivatives with the gradient Compute the directional derivative of the... Problem 22E Problem 23E: Computing directional derivatives with the gradient Compute the directional derivative of the... Problem 24E: Computing directional derivatives with the gradient Compute the directional derivative of the... Problem 25E: Computing directional derivatives with the gradient Compute the directional derivative of the... Problem 26E: Computing directional derivatives with the gradient Compute the directional derivative of the... Problem 27E: Direction of steepest ascent and descent Consider the following functions and points P a. Find the... Problem 28E: Direction of steepest ascent and descent Consider the following functions and points P a. Find the... Problem 29E: Direction of steepest ascent and descent Consider the following functions and points P a. Find the... Problem 30E: Direction of steepest ascent and descent Consider the following functions and points P a. Find the... Problem 31E: Direction of steepest ascent and descent Consider the following functions and points P a. Find the... Problem 32E: Direction of steepest ascent and descent Consider the following functions and points P a.Find the... Problem 33E: Interpreting directional derivatives A function f and a point P are given. Let correspond to the... Problem 34E: Interpreting directional derivatives A function f and a point P are given. Let correspond to the... Problem 35E: Interpreting directional derivatives A function f and a point P are given. Let correspond to the... Problem 36E: Interpreting directional derivatives A function f and a point P are given. Let correspond to the... Problem 37E: Interpreting directional derivatives A function f and a point P are given. Let correspond to the... Problem 38E: Interpreting directional derivatives A function f and a point P are given. Let correspond to the... Problem 39E Problem 40E Problem 41E Problem 42E Problem 43E: Level curves Consider the paraboloid f(x, y) = 16 x2/4 y,2/16 and the point P on the given level... Problem 44E: Level curves Consider the paraboloid f(x, y) = 16 x2/4 y,2/16 and the point P on the given level... Problem 45E: Level curves Consider the paraboloid f(x, y) = 16 x2/4 y,2/16 and the point P on the given level... Problem 46E: Level curves Consider the paraboloid f(x, y) = 16 x2/4 y,2/16 and the point P on the given level... Problem 47E: Level curves Consider the upper half of the ellipsoid f(x,y)=1x24y216 and the point P on the given... Problem 48E: Level curves Consider the upper half of the ellipsoid f(x,y)=1x24y216 and the point P on the given... Problem 49E: Level curves Consider the upper half of the ellipsoid f(x,y)=1x24y216 and the point P on the given... Problem 50E Problem 51E: Path of steepest descent Consider each of the following surfaces and the point P on the surface. a.... Problem 52E: Path of steepest descent Consider each of the following surfaces and the point P on the surface. a.... Problem 53E: Path of steepest descent Consider each of the following surfaces and the point P on the surface. a.... Problem 54E: Path of steepest descent Consider each of the following surfaces and the point P on the surface. a.... Problem 55E: Gradients in three dimensions Consider the following functions f, points P, and unit vectors u. a.... Problem 56E: Gradients in three dimensions Consider the following functions f, points P, and unit vectors u. a.... Problem 57E: Gradients in three dimensions Consider the following functions f, points P, and unit vectors u. a.... Problem 58E: Gradients in three dimensions Consider the following functions f, points P, and unit vectors u. a.... Problem 59E: Gradients in three dimensions Consider the following functions f, points P, and unit vectors u. a.... Problem 60E: Gradients in three dimensions Consider the following functions f, points P, and unit vectors u. a.... Problem 61E: Gradients in three dimensions Consider the following functions f, points P, and unit vectors u. a.... Problem 62E: Gradients in three dimensions Consider the following functions f, points P, and unit vectors u. a.... Problem 63E: Explain why or why not Determine whether the following statements are true and give an explanation... Problem 64E: Gradient of a composite function Consider the function F(x,y,z)=exyz. a. Write F as a composite... Problem 65E: Directions of zero change Find the directions in the xy-plane in which the following functions have... Problem 66E Problem 67E: Directions of zero change Find the directions in the xy-plane in which the following functions have... Problem 68E: Directions of zero change Find the directions in the xy-plane in which the following functions have... Problem 69E: Steepest ascent on a plane Suppose a long sloping hillside is described by the plane z = ax + by +... Problem 70E: Gradient of a distance function Let (a, b) be a given point in R2 and let d = f(x,y) be the distance... Problem 71E: Looking aheadtangent planes Consider the following surfaces f(x, y, z) = 0, which may be regarded as... Problem 72E Problem 73E: Looking aheadtangent planes Consider the following surfaces f(x, y, z) = 0, which may be regarded as... Problem 74E Problem 75E Problem 76E Problem 77E Problem 78E Problem 79E Problem 80E Problem 81E: Rules for gradients Use the definition of the gradient (in two or three dimensions), assume that f... Problem 82E Problem 83E Problem 84E Problem 85E Problem 86E Problem 87E format_list_bulleted