Calculus 3

Section 11.5: Problem 1 [1 point] Suppose w = E + E, where y z: z = 3'\Section 11.5: Problem 2 (1 point) Suppose z = x'sin(y) , x = 48 -t', y = -6st. A. Use the chain rule to find Oz and DE as functions of , y, s and t. Oz Oz B. Find the numerical values of D's and when (s, t) = (5, 4). dis (5, 4) = Oz of (5, 4) =Section 11.5: Problem 3 (1 point) Use the chain rule to find = and - TH , Where 7s z = etan(y), x = 2s + 2t, y = 3t First the pieces: Oz Dz Dy And putting it all together: Oz Dz dy Oz Or. Oz dy Dy Us and = Dy Ut\fSection 11.5: Problem 5 (1 point) Let W(s, t) = F(u(s, t), v(s, t)) where u(1, 0) = -4, us(1, 0) = -8, u (1, 0) = 9 v(1, 0) = -5, vs(1, 0) = -2, v.(1, 0) = 1 Fu(-4, -5) = -1, Fo(-4, -5) = 5 Ws(1, 0) = We(1, 0) =Section 11.5: Problem 6 {1 point} Consider the curve :3 + Hwy + y\" = B The equation of the tangent line to the curve at the point {1, 1] has the form y 2 mm + b where m=Bandh=D Section 11.5: Problem 7 (1 point) Consider the surface F(x, y, 2) = x32 + sin(1 28) -1 =0. Find the following partial derivatives Oz 542.87Section 11.5: Problem 8 (1 point) The radius of a right circular cone is increasing at a rate 0T4 inches per second and its height is decreasing at a rate of 3 inches per second. At what rate is the volume of the cone changing when the radius is 30 inches and the height is 20 inches? NOTE The volume of a cane with base radius r and height h is given by V = %m2h C] cubic inches per second Section 11.5: Problem 9 (1 point) In a simple electric circuit, Ohm's law states that V = IR, where V is the voltage in Volts, I is the current in Amperes, and R is the resistance in Ohms. Assume that, as the battery wears out, the voltage decreases at 0.02 Volts per second and, as the resistor heats up, the resistance is increasing at 0.02 Ohms per second. When the resistance is 100 Ohms and the current is 0.04 Amperes, at what rate is the current changing? Amperes per second