MATH114 Lecture Notes - Lecture 11: Indeterminate Form, Intermediate Value Theorem
29 Sep 2018
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Informally, a function is continuous if you can draw its graph without lifting your pen. For example, the function y = x + 3 is continuous. Note: previously, when stating the limit around a point, we gave answers such as , however this was just to provide more information as technically the limit at that point dne because infinity is an indefinite number. In continuity, the limit has to exist, so functions approaching infinity at that point should be written as dne, and are a type of discontinuity as seen below. Functions can also be continuous from the right only and from the left only: For example, (cid:1858)(cid:4666)(cid:4667)= is a function that is right continuous at a point x. Removable discontinuity can be removed by defining another function at that point (cid:1858)(cid:4666)(cid:4667)= (cid:2870) (cid:883) Infinite discontinuity the limit function approaches positive or negative infinity (cid:1858)(cid:4666)(cid:4667)= (cid:883)(cid:2870) lim (cid:2868)(cid:1858)(cid:4666)(cid:4667) (cid:1830)(cid:1831)
