MAT 21A Lecture 5: MAT 21A Lecture Notes 10-08-2018

• School: UC-Davis
• Department: Mathematics
• Course: MAT 21A
• Professor: Korana Burke

Document Summary

Let c be a real number that is either an interior point or an end point of an interval in the domain of f. The function f is continuous at c if lim (cid:1858)(cid:4666)(cid:4667)=(cid:1858)(cid:4666)(cid:1855)(cid:4667: the function f is right continuous at c if lim +(cid:1858)(cid:4666)(cid:4667)=(cid:1858)(cid:4666)(cid:1855)(cid:4667, the function f is left continuous at c if lim (cid:1858)(cid:4666)(cid:4667)=(cid:1858)(cid:4666)(cid:1855)(cid:4667) (cid:1871)(cid:1855)(cid:1867)(cid:1866)(cid:1872)(cid:1866)(cid:1873)(cid:1867)(cid:1873)(cid:1871) (cid:1853)(cid:1872) =2 (cid:1858)(cid:4666)(cid:4667)= 2 2. The above function is discontinuous at x=2 because f(2) does not exist. Thus, there is a hole at x=2, so the function is not continuous. A function f(x) is continuous at a point x=c only if it meets the following 3 criteria: Continuity test: f(c) exists, lim (cid:1858)(cid:4666)(cid:4667) exists, lim (cid:1858)(cid:4666)(cid:4667)=(cid:1858)(cid:4666)(cid:1855)(cid:4667) If f is continuous at c and g is continuous at f(c), then the composition (cid:1859) (cid:1858) is. If lim (cid:1858)(cid:4666)(cid:4667)=(cid:1854) and (cid:1859) is continuous at (cid:1854), then lim (cid:1859)((cid:1858)(cid:4666)(cid:4667))=(cid:1859)(cid:4666)(cid:1854)(cid:4667)