MATH116 Lecture 1: M116F15_T9sol
9 Dec 2015
School
Department
Course
Professor
Document Summary
Tutorial solutions 9: use di erentials (or a linearization) to estimate the value of. Solution: here it should be clear that we want to use x = 144 as our point of tangency. Doing this with the function f (x) = x we have (for general x) f (x) = f (144) + y. 150 = f (150) we have f (150) 12 + = 12. 25 or: approximate the area under the curve of the function y = [0, 2], by dividing the interval into 5 equal parts, and making rectangles touching the curve at sample points in the interval. We have x = 2 x4 = 1. 6, and x5 = 2. 5, and xi = 0 + i x = 2i. That is, x0 = 0, x1 = 0. 4, x2 = 0. 8, x3 = 1. 2, (a) the area using left endpoints is: = 2. 648219196 2. 648 (b) the area using right endpoints is: f (xi) x =
