MATH 200 Study Guide - Midterm Guide: Hypotenuse, Cylindrical Coordinate System, Function Composition

• School: UBC
• Department: Mathematics
• Course: MATH 200
• Professor: All

Document Summary

[10: one side of a right triangle is measured to be 3 with a maximum possible error of. 0. 1, and the other side is measured to be 4 with a maximum possible error of 0. 2. Use the di erential or linear approximation to estimate the maximum possible error in calculating the length of the hypotenuse of the right triangle. [10: assume that f (x, y) satis es laplace"s equation. Show that this is also the case for the composite function g(s, t) = f (s t, s + t). You may assume that f (x, y) is a smooth function so that the chain. Rule and clairaut"s theorem on the equality of the mixed partials derivatives apply. [10: you are standing at a location where the surface of the earth is smooth. The slope in the southern direction is 4 and the slope in the south-eastern direction is 2.