Problem 1RCC: (a) What is a function of two variables? (b) Describe three methods for visualizing a function of... Problem 2RCC Problem 3RCC Problem 4RCC: (a) What does it mean to say that f is continuous at (a, b)? (b) If f is continuous on 2, what can... Problem 5RCC Problem 6RCC Problem 7RCC Problem 8RCC Problem 9RCC Problem 10RCC: If z = f(x, y), what arc the differentials dx, dy, and dz? Problem 11RCC Problem 12RCC: If z is defined implicitly as a function of x and y by an equation of the form F(x, y, z) = 0, how... Problem 13RCC Problem 14RCC Problem 15RCC Problem 16RCC Problem 17RCC Problem 18RCC Problem 19RCC Problem 1RQ Problem 2RQ Problem 3RQ Problem 4RQ Problem 5RQ Problem 6RQ: Determine whether the statement is true or false. If it is true, explain why. If it is false,... Problem 7RQ Problem 8RQ Problem 9RQ: Determine whether the statement is true or false. If it is true, explain why. If it is false,... Problem 10RQ Problem 11RQ Problem 12RQ Problem 1RE Problem 2RE: Find and sketch the domain of the function. 2. f(x,y)=4x2y2+1x2 Problem 3RE Problem 4RE Problem 5RE: Sketch several level curves of the function. 5. f(x,y)=4x2+y2 Problem 6RE: Sketch several level curves of the function. 6. f(x, y) = ex + y Problem 7RE: Make a rough sketch of a contour map for the function whose graph is shown. Problem 8RE: The contour map of a function f is shown, (a) Estimate the value of f(3, 2). (b) Is fx(3, 2)... Problem 9RE Problem 10RE Problem 11RE Problem 12RE Problem 13RE Problem 14RE Problem 15RE Problem 16RE Problem 17RE Problem 18RE: The speed of sound traveling through ocean water is a function of temperature, salinity, and... Problem 19RE Problem 20RE Problem 21RE Problem 22RE Problem 23RE Problem 24RE Problem 25RE: Find equations of (a) the tangent plane and (b) the normal line to the given surface at the... Problem 26RE Problem 27RE Problem 28RE: Find equations of (a) the tangent plane and (b) the normal line to the given surface at the... Problem 29RE: Find equations of (a) the tangent plane and (b) the normal line to the given surface at the... Problem 30RE Problem 31RE: Find the points on the hyperboloid x2 + 4y2 z2 = 4 where the tangent plane is parallel to the plane... Problem 32RE Problem 33RE: Find the linear approximation of the function f(x,y,z)=x3y2+z2 at the point (2, 3, 4) and use it to... Problem 34RE: The two legs of a right triangle are measured as 5 m and 12 m with a possible error in measurement... Problem 35RE Problem 36RE: If v = x2sin y + yexy, where x = s + 2t and y = st, use the Chain Rule to find v/s and v/t when s =... Problem 37RE: Suppose z = f(x, y), where x = g(s, t), y = h(s, t), g(1, 2) = 3, gs(1, 2) = 1, gt(1,2) = 4, h(1, 2)... Problem 38RE Problem 39RE Problem 40RE Problem 41RE Problem 42RE: If cos(xyz) = 1 + .x2y2 + z2, find zx and zy. Problem 43RE: Find the gradient of the function f(x,y,z)=x2eyz2. Problem 44RE Problem 45RE Problem 46RE: Find the directional derivative of f at the given point in the indicated direction. 46.... Problem 47RE Problem 48RE Problem 49RE: The contour map shows wind speed in knots during Hurricane Andrew on August 24, 1992. Use it to... Problem 50RE: Find parametric equations of the tangent line at the point (2, 2, 4) to the curve of intersection of... Problem 51RE Problem 52RE Problem 53RE Problem 54RE Problem 55RE: Find the absolute maximum and minimum values of f on the set D. 55. f(x, y) = 4xy2 x2y2 xy3; D is... Problem 56RE: Find the absolute maximum and minimum values of f on the set D. 55. f(x,y)=ex2y2(x2+2y2); D is the... Problem 57RE Problem 58RE: Use a graphing calculator or computer (or Newtons method or a computer algebra system) to find the... Problem 59RE Problem 60RE Problem 61RE Problem 62RE: Use Lagrange multipliers to find the maximum and minimum values of f subject to the given... Problem 63RE Problem 64RE: A package in the shape of a rectangular box can be mailed by the US Postal Service if the sum of its... Problem 65RE: A pentagon is formed by placing an isosceles triangle on a rectangle, as shown in the figure. II the... Problem 1P: A rectangle with length L and width W is cut into four smaller rectangles by two lines parallel to... Problem 2P: Marine biologists have determined that when a shark detects the presence of blood in the water, it... Problem 3P: A long piece of galvanized sheet metal with width w is to be bent into a symmetric form with three... Problem 4P: For what values of the number r is the function... Problem 5P: Suppose f is a differentiable function of one variable. Show that all tangent planes to the surface... Problem 6P: (a) Newton's method for approximating a root of an equation f(x) = 0 (see Section 4.8) can be... Problem 7P: If the ellipse x2/a2 + y2/b2 = 1 is to enclose the circle x2 + y2 = 2y, what values of a and b... Problem 8P format_list_bulleted