MATH 234 Lecture 11: MATH234_Lecture11(1)

• School: UW-Madison
• Department: Mathematics
• Course: MATH 234
• Professor: Betsy Stovall

Document Summary

Let (cid:1858)(cid:4666)(cid:1876)(cid:4667) be a function of two variables. Let 2 be the domain of definition of (cid:1858)(cid:4666)(cid:1876),(cid:1877)(cid:4667) is the maximal subset on the plane where (cid:1858) (cid:3028) or (cid:1858) makes sense (cid:1858)(cid:4666)(cid:1876),(cid:1877)(cid:4667)= (cid:1876)(cid:1877) We need (cid:1876)(cid:1877)(cid:3410)(cid:882) is the set of all points (cid:4666)(cid:1876),(cid:1877)(cid:4667) so that (cid:1876)(cid:1877)>(cid:882) Problem is when (cid:1876)+(cid:1877) (cid:884)=(cid:882) is the plane minus line (cid:1876)+(cid:1877)=(cid:884) The domain of function is the set of all points (cid:4666)(cid:1876),(cid:1877)(cid:4667) so that (cid:1876)+(cid:1877) (cid:1878) (cid:882) Let (cid:1858)(cid:4666)(cid:1876),(cid:1877)(cid:4667) be a function with domain of definition and let (cid:4666)(cid:1853),(cid:1854)(cid:4667) be a point in. Disk centered at a point (cid:4666)(cid:1853),(cid:1854)(cid:4667) of the radius (cid:1870) is the set of all the points with coordinated (cid:4666)(cid:1876),(cid:1877)(cid:4667) satisfying condition (x,y) (a,b) Distance between fixed point (cid:4666)(cid:1853),(cid:1854)(cid:4667) and (cid:4666)(cid:1876),(cid:1877)(cid:4667) is (cid:3409)(cid:1870)2 (cid:1856)(cid:1871)(cid:1872)= (cid:4666)(cid:1876) (cid:1853)(cid:4667)2+(cid:4666)(cid:1877) (cid:1854)(cid:4667)2. Which is the distance between (cid:4666)(cid:1853),(cid:1854)(cid:4667) and (cid:4666)(cid:1876),(cid:1877)(cid:4667) and show that the distance (cid:3409)(cid:1870)2. The disk of radius (cid:1870) centered at (cid:4666)(cid:1853),(cid:1854)(cid:4667) is.