MAT 21C Study Guide - Midterm Guide: Curve, Saddle Point, Maxima And Minima

• School: UC-Davis
• Department: Mathematics
• Course: MAT 21C
• Professor: All

Document Summary

Find the following limit, if it exists: x + y " 4 x + y " 2 lim (x,y) "(2,2) where the domain is everything with x + y 0 and x + y 6= 4. R. (b) find the absolute extreme values of f on all of r. Find the curvature for times t > 0 for the space curve r(t) = (cos t + t sin t)i + (sin t " t cos t)j + 3k. Solution: v(t) = ( " sin t + sin t + t cos t)i + (cos t " cos t + t sin t)j = t cos ti + t sin tj, so. |v(t)| = p t2 cos2 t + t2 sin2 t = t2 = t, and the unit tangent vector is given by. T = " sin tt + cos tj, d dt. | " sin tt + cos tj| =