Calculus 1000A/B Lecture Notes - Lecture 13: Asymptote, Piecewise, Oliver Heaviside

• School: Western University
• Department: Calculus
• Course: Calculus 1000A/B
• Professor: Kiriushcheva

Document Summary

Calculus 1000a lecture 12/13 - section 2. 5- continuity. Continuity is an important property of a function in calculus, especially when it comes to derivatives- we can only find the derivatives of continuous functions. Definition: a function is continuous at point (cid:858)a(cid:859) if it satisfies each of the following three properties: lim (cid:1858)(cid:4666)(cid:1876)(cid:4667)=(cid:1858)(cid:4666)(cid:1853)(cid:4667) (2) the limit of f(x) exists (1) f(a) is defined (3) lim (cid:1858)(cid:4666)(cid:1876)(cid:4667)=(cid:1858)(cid:4666)(cid:1853)(cid:4667) If one of these properties isn"t satisfied, the function is discontinuous or has discontinuity at point a", though it may be continuous at other points. These two values would be equal, thus the function is continuous at this point: on the left and right sides of the graph, the function heads to + and - , respectively. At these points, it would be approaching a vertical asymptote, and therefore would be discontinuous at that point. Figure 1: jump discontinuity, image courtesy of wikipedia.