MATH 102 Lecture Notes - Lecture 5: Linear Approximation, Aphid

• School: UBC
• Department: Mathematics
• Course: MATH 102
• Professor: Elyse Yeager

Document Summary

Linear approximation tangent line to the curve y= text at point xo is y= filxo) (x - xo) + f /xo line intersects x-axis at. Int = = . F f / (xo) ex . flx) (cid:12200)*33*55*-55. Want to find its root: what is f- 11, tangent line of f-1 1 at = i intersect -axis ( ,) f- 111--1113+5111-5=1. = 1: determine if f- 1 11 is. Closer to 0 than fl1) f- 111=1 f / 1) = f- 0. 04 f " / 1=3 2+5 n looking for -valve. * if you find root of tangent line , you"re close to the root of the function. Iteration : want to guess root of fix) , use that location to take tangent line. Guess root (xo) of f- 1 1 using newton "s method to approximate roots. = 0 want : start close to a root.