How to Determine If a Function is Continuous on a Graph

Continuous function - Conditions, Discontinuities, and Examples

SOLVED:a. Suppose the graph of a continuous function f(x) rises steadily as x moves from left to right across an interval [a, b] . Let P be a partition of [a, b] into n subintervals of equal length Δx=(b-a) / n . Show by referring to the accompanying figure that the difference between the upper and lower sums for f on this partition can be represented graphically as the area of a rectangle R whose dimensions are [f(b)-f(a)] by Δx (Hint: The difference U-L is the sum of areas of rectangles whose