MATH 154 Lecture 16: Linear Approximation & Newton's Method

• School: Simon Fraser University
• Department: Mathematics
• Course: MATH 154
• Professor: Yusuf Tuncer

Document Summary

With linear approximations, we are guessing based on values that we know. The linearization of a function at a point a is the function given by the tangent line at a. We have the point (100, 10), so we can get the equation of the tangent line at that point. If x is close to a, then la(x) is approximately equal to f(x) F(x) is the actual value, l(x) is the approximation. The difference between f(x) and l(x), which should ideally be small. If we have (cid:883)(cid:882)(cid:883), it should be close to (cid:883)(cid:882)(cid:882) on the graph of (cid:4666)(cid:1876)(cid:4667)= (cid:1876) We know (cid:886)(cid:891) is 7, so we can use that for the approximation. If we have a function (cid:4666)(cid:1876)(cid:4667)=(cid:885)(cid:1876)(cid:2873) (cid:884)(cid:1876)(cid:2871) (cid:889)(cid:1876) & say our initial estimate is 2, we can. Newton"s method is for approximating zeroes of a function that are close to xo use newton"s method to get approximations.