MATH137 Lecture : Newton's Method, Riemann Sums, Definite Integrals

• School: University of Waterloo
• Department: Mathematics
• Course: MATH137
• Professor: Jennifer Nissen

Document Summary

Root finding can be easy or tough to do, sometimes even impossible. Initial approximation of is the tangent to curve at. Use tangent to at , take the -intercept. Since is closer to than let be the next approximation. In general, if approximation is and , the next approximation is. Accurate to decimal places iff 2 approximation in a row agrees to decimal places. So root is , accurate to 4 decimal places. Lec 29 - the area problem, riemann sums. Find the area of the region what lies under from to . Approximate the area under from 0 to 1 using riemann sums using 6 intervals and. Divide up into subintervals, the width of each is. Using right endpoints, are a of rectangle is. Area under the curve is approximately this is the right riemann sum with subintervals. as this approximately gets better is the left riemann sum with subintervals.