MA 141 Study Guide - Final Guide: Tangent, Classification Of Discontinuities
Document Summary
In general, we like to work with "nice" functions. We are building tools to properly de ne continuous functions. Non-rigorously, what is a continuous function: can be drawn without picking pen up o the paper, only needs to apply for speci ed domain - might be weird outside domain, examples: sine and cosine, polynomials, exponential functions. Here is the graph of f (x) = sin x on h 11 . Here, f (x) = sin x is contin- uous at the point x = be- cause it has no break. Observation: if f is de ned on an open interval i and is continuous at x0 i, then as the variable x approaches x0 from both sides, the values of f (x) approach the value f (x0). We denote this as lim x x0 f (x) = f (x0). = 1, this observation says that as our x values get closer to.
