Problem 1E: Suppose you are standing on the surface z = f(x, y) at the point (a, b, f(a, b)). Interpret the... Problem 2E Problem 3E Problem 4E Problem 5E Problem 6E: The volume of a right circular cylinder with radius r and height h is V = r2h. Is the volume an... Problem 7E Problem 8E Problem 9E Problem 10E Problem 11E Problem 12E Problem 13E Problem 14E Problem 15E Problem 16E Problem 17E Problem 18E Problem 19E Problem 20E Problem 21E Problem 22E Problem 23E Problem 24E Problem 25E Problem 26E Problem 27E Problem 28E Problem 29E Problem 30E Problem 31E Problem 32E Problem 33E Problem 34E Problem 35E Problem 36E Problem 37E Problem 38E Problem 39E Problem 40E Problem 41E Problem 42E Problem 43E Problem 44E: Equality of mixed partial derivatives Verify that fxy = fyx for the following functions.... Problem 45E Problem 46E Problem 47E Problem 48E Problem 49E Problem 50E Problem 51E Problem 52E Problem 53E Problem 54E Problem 55E: Gas law calculations Consider the Ideal Gas Law PV = kT, where k 0 is a constant. Solve this... Problem 56E Problem 57E: Nondifferentiability? Consider the following functions f. a.Is f continuous at (0, 0)? b.Is f... Problem 58E: Nondifferentiability? Consider the following functions f. a.Is f continuous at (0, 0)? b.Is f... Problem 59E Problem 60E Problem 61E Problem 62E Problem 63E Problem 64E Problem 65E Problem 66E: Miscellaneous partial derivatives Compute the first part derivatives of the following functions.... Problem 67E Problem 68E Problem 69E Problem 70E: Spherical caps The volume of the cap of a sphere of radius r and thickness h is V=3h2(3rh), for 0 h... Problem 71E Problem 72E: Body mass index The body mass index (BMI) for an adult human is given by the function B = w/h2,... Problem 73E: Electric potential function The electric potential in the xy-plane associated with two positive... Problem 74E Problem 75E: Resistors in parallel Two resistors in an electrical circuit with resistance R1 and R2 wired in... Problem 76E: Wave on a string Imagine a string that is fixed at both ends (for example, a guitar string). When... Problem 77E: Wave equation Traveling waves (for example, water waves or electromagnetic waves) exhibit periodic... Problem 78E: Wave equation Traveling waves (for example, water waves or electromagnetic waves) exhibit periodic... Problem 79E: Wave equation Traveling waves (for example, water waves or electromagnetic waves) exhibit periodic... Problem 80E: Laplaces equation A classical equation of mathematics is Laplaces equation, which arises in both... Problem 81E: Laplaces equation A classical equation of mathematics is Laplaces equation, which arises in both... Problem 82E: Laplaces equation A classical equation of mathematics is Laplaces equation, which arises in both... Problem 83E: Laplaces equation A classical equation of mathematics is Laplaces equation, which arises in both... Problem 84E: Heat equation The flow of hear along a thin conducting bar is governed by the one-dimensional heal... Problem 85E: Heat equation The flow of hear along a thin conducting bar is governed by the one-dimensional heal... Problem 86E Problem 87E: Heat equation The flow of hear along a thin conducting bar is governed by the one-dimensional heal... Problem 88E Problem 89E: Differentiability Use the definition of differentiability to prove that the following functions are... Problem 90E: Nondifferentiability? Consider the following functions f. a.Is f continuous at (0, 0)? b.Is f... Problem 91E: Nondifferentiability? Consider the following functions f. a.Is f continuous at (0, 0)? b.Is f... Problem 92E Problem 93E: Derivatives of an integral Let h be continuous for all real numbers. a.Find fx and fy when f(x, y) =... Problem 94E Problem 95E format_list_bulleted