Problem 1E: Suppose n is a vector normal to the tangent plane of the surface F(x, y, z) = 0 at a point. How is n... Problem 2E: Write the explicit function z = xy2 + x2y 10 in the implicit form F(x, y, z) = 0. Problem 3E: Write an equation for the plane tangent to the surface F(x, y, z) = 0 at the point (a, b, c) Problem 4E Problem 5E: Explain how to approximate a function f at a point near (a, b) where the values of f, fx, and fy are... Problem 6E: Explain how to approximate the change in a function f when the independent variables change from (a,... Problem 7E: Write the approximate change formula for a function z = f(x, y) at the point (a, b) in terms of... Problem 8E: Write the differential dw for the function w = f(x, y, z). Problem 9E: Tangent planes for F(x,y,z) = 0 Find an equation of the plane tangent to the following surfaces at... Problem 10E: Tangent planes for F(x,y,z) = 0 Find an equation of the plane tangent to the following surfaces at... Problem 11E: Tangent planes for F(x,y,z) = 0 Find an equation of the plane tangent to the following surfaces at... Problem 12E: Tangent planes for F(x,y,z) = 0 Find an equation of the plane tangent to the following surfaces at... Problem 13E: Tangent planes for F(x,y,z) = 0 Find an equation of the plane tangent to the following surfaces at... Problem 14E: Tangent planes for F(x, y, z) = 0 Find an equation of the plane tangent to the following surfaces at... Problem 15E: Tangent planes for F(x, y, z) = 0 Find an equation of the plane tangent to the following surfaces at... Problem 16E: Tangent planes for F(x, y, z) = 0 Find an equation of the plane tangent to the following surfaces at... Problem 17E: Tangent planes for z = f (x, y) Find an equation of the plane tangent to the following surfaces at... Problem 18E: Tangent planes for z = f (x, y) Find an equation of the plane tangent to the following surfaces at... Problem 19E: Tangent planes for z = f (x, y) Find an equation of the plane tangent to the following surfaces at... Problem 20E: Tangent planes for z = f (x, y) Find an equation of the plane tangent to the following surfaces at... Problem 21E: Tangent planes for z = f (x, y) Find an equation of the plane tangent to the following surfaces at... Problem 22E Problem 23E: Tangent planes for z = f (x, y) Find an equation of the plane tangent to the following surfaces at... Problem 24E: Tangent planes for z = f (x, y) Find an equation of the plane tangent to the following surfaces at... Problem 25E: Linear approximation a.Find the linear approximation to the function f at the given point. b.Use... Problem 26E: Linear approximation a.Find the linear approximation to the function f at the given point. b.Use... Problem 27E: Linear approximation a.Find the linear approximation to the function f at the given point. b.Use... Problem 28E: Linear approximation a.Find the linear approximation to the function f at the given point. b.Use... Problem 29E: Linear approximation a.Find the linear approximation to the function f at the given point. b.Use... Problem 30E Problem 31E: Approximate function change Use differentials to approximate the change in z for the given changes... Problem 32E: Approximate function change Use differentials to approximate the change in z for the given changes... Problem 33E: Approximate function change Use differentials to approximate the change in z for the given changes... Problem 34E: Approximate function change Use differentials to approximate the change in z for the given changes... Problem 35E: Changes in torus surface area The surface area of a torus with an inner radius r and an outer radius... Problem 36E: Changes in cone volume The volume of a right circular cone with radius r and height h is V=r2h/3.... Problem 37E: Area of an ellipse The area of an ellipse with axes of length 2a and 2b is A = ab Approximate the... Problem 38E: Volume of a paraboloid The volume of a segment of a circular paraboloid (see figure) with radius r... Problem 39E: Differentials with more than two variables Write the differential dw in terms of the differentials... Problem 40E: Differentials with more than two variables Write the differential dw in terms of the differentials... Problem 41E: Differentials with more than two variables Write the differential dw in terms of the differentials... Problem 42E: Differentials with more than two variables Write the differential dw in terms of the differentials... Problem 43E: Law of Cosines The side lengths of any triangle are related by the Law of Cosines. c2 = a2 + b2 2ab... Problem 44E Problem 45E: Explain why or why not Determine whether the following statements are true and give an explanation... Problem 46E: Tangent planes Find an equation of the plane tangent to the following surfaces at the given point.... Problem 47E: Tangent planes Find an equation of the plane tangent to the following surfaces at the given point.... Problem 48E: Tangent planes Find an equation of the plane tangent to the following surfaces at the given point.... Problem 49E: Tangent planes Find an equation of the plane tangent to the following surfaces at the given point.... Problem 50E: Horizontal tangent planes Find the points at which the following surfaces have horizontal tangent... Problem 51E: Horizontal tangent planes Find the points at which the following surfaces have horizontal tangent... Problem 52E: Horizontal tangent planes Find the points at which the following surfaces have horizontal tangent... Problem 53E: Horizontal tangent planes Find the points at which the following surfaces have horizontal tangent... Problem 54E Problem 55E: Surface area of a cone A cone with height h and radius r has a lateral surface area (the curved... Problem 56E: Line tangent to an intersection curve Consider the paraboloid z = x2 + 3y2 and the plane z = x + y +... Problem 57E Problem 58E: Water-level changes A conical tank with radius 0.50 m and height 2.00 m is filled with water (see... Problem 59E Problem 60E: Floating-point operations In general, real numbers (with infinite decimal expansions) cannot be... Problem 61E: Probability of at least one encounter Suppose that in a large group of people, a fraction 0 r 1 of... Problem 62E Problem 63E Problem 64E Problem 65E: Logarithmic differentials Let f be a differentiable function of one or more variables that is... Problem 66E format_list_bulleted