ll AT&T ? 3:05 PM coursesite.lehigh.edu 1 of 1 MATH 023 Calculus III Spring 2020 Written Problem Set 6 Due Wednesday, February 26th for the M/W classes Due Thursday February 27th for the Tu/Th classes PART I (Practice Problems, Very Important but are not to be handed in) • $14.1 # 1, 9, 15, 25, 32, 53, 61-66 (matching), 69 • $14.2 # 1, 7, 9, 11, 13, 25, 33, 39, 41 • $14.3 # 5, 7, 11, 15, 17, 19, 25, 27, 29, 33, 37, 49, 57, 59, 65, 75, 97 PART II (required problems to be handed in) • $14.1 # 10, 22, 26, 30, 44, 48, 54, 70 (Sketch several contour surfaces f(r. y, z) = c for e> 0, c = 0 and e<0 on the same set of axes) • $14.2 # 10, 18, 36 (and sketch the set), 38 • $14.3 # 12, 30, 32, 42, 44, 50, 56, 68, 74, 78a, 88, 100abc • Non-Book Problems 1. Find lim sin(43y) (a)-(0o) tan(7247 2. Partial derivatives are not only about what independent variable is varying. but which are held fixed. (a) Consider r and y as functions of polar coordinates r and 6. Find and (b) Now, suppose you want to vary e, keeping r fired. Express y in terms of (same as saying as a function of) z and 0. Then find with a held fixed. (c) Express each of your answers for in terms of r and 6. Do they agree? (This is a warning about notation. What you really did was the following: y = f (r, 6) from part (a), whereas y = g(r,6) from part (b). You really computed f and . OK, when you say it that way..but they are both "y"! Again, which variable(s) move and which are held fixed?!) 3. Draw a triangle with sides labelled a, b and e, and angle e opposite c. Recall your favorite Law (of Cosines): 2 = a² + - 2abcos e. This relationship defines 8 implicitly as a function of a, b and e. (a) Two students in class almost came to fisticuffs over the following: Student 1 said that = 0, because they said they could vary side a without changing the angle. Student 2 disagreed. Explain using pictures (and a few words) who is correct. (b) Use implicit differentiation to find expressions for . and in terms of a, b, c and 0.