- Limit – The value that a function or expression approaches as the domain variable(s) approach a specific value. Limits are written in the form
- Continuous Function – A function with a connected graph.
- Piecewise Continuous Function – A function made up of a finite number of continuous pieces. Piecewise continuous functions may not have vertical asymptotes. In fact, the only possible types of discontinuities for a piecewise continuous function are removable and step discontinuities.
- Intermediate Value Theorem (IVT) – A theorem verifying that the graph of a continuous function is connected.
- Discontinuous Function – A function with a graph that is not connected.
- Removable Discontinuity – A hole in a graph. That is, a discontinuity that can be “repaired” by filling in a single point. In other words, a removable discontinuity is a point at which a graph is not connected but can be made connected by filling in a single point. Formally, a removable discontinuity is one at which the limit of the function exists but does not equal the value of the function at that point; this may be because the function does not exist at that point.
- Essential Discontinuity – Any discontinuity that is not removable. That is, a place where a graph is not connected and cannot be made connected simply by filling in a single point. Step discontinuities and vertical asymptotes are two types of essential discontinuities. Formally, an essential discontinuity is a discontinuity at which the limit of the function does not exist.
- One-Sided Limit – Either a limit from the left or a limit from the right.
- Asymptote – A line or curve that the graph of a relation approaches more and more closely the further the graph is followed. Note: Sometimes a graph will cross a horizontal asymptote or an oblique asymptote. The graph of a function, however, will never cross a vertical asymptote.
- Infinite Limit – A limit that has an infinite result (either ∞ or –∞ ), or a limit taken as the variable approaches ∞ (infinity) or –∞ (minus infinity). The limit can be one-sided.
Chapter 2: Limits
Assignment Log
Handouts
2.1 Limits, Rates of Change, and Tangent Lines
2.2 Limits: A Numerical and Graphical Approach
2.3 Basic Limit Laws
2.4 Limits and Continuity
2.5 Evaluating Limits Algebraically
#1, 7, 9, 11, 17, 19, 25, 27, 33, 35, 39, 47
answers
2.6 Trigonometric Limits
2.7 Limits at Infinity
2.8 Intermediate Value Theorem
Handouts
2.1 Limits, Rates of Change, and Tangent Lines
2.2 Limits: A Numerical and Graphical Approach
2.3 Basic Limit Laws
2.4 Limits and Continuity
2.5 Evaluating Limits Algebraically
#1, 7, 9, 11, 17, 19, 25, 27, 33, 35, 39, 47
answers
2.6 Trigonometric Limits
2.7 Limits at Infinity
2.8 Intermediate Value Theorem