MATH 215 Midterm: exam1f15
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Fall 2015, math 215 calculus iii, exam 1. 1. (a) (5 points) the planes 2x 2y + z = 3 and 4x + 4y 2z = 6 are parallel to each other. Find the distance between them. (b) (5 points) let be the angle between the plane 2x 2y + z = 3 and the plane x + y + z = 0. There is no need for explanation. (a) (b) (c) (d) (e) (f ) (g) (h) (i) (1) (2 points) which picture represents the level curves of f (x, y) = Consider the curve c given by the intersection of the plane x = 2 and the surface z = f (x, y). The resistance r, on the other hand, is slowly increasing as the resistor heats up. The voltage v , the resistance r, and the current i satisfy ohm"s law v = ir.
