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What are the differences between removable and infinite discontinuities?
Removable: Limit exists, can be 'fixed'. Infinite: Vertical asymptote, limit DNE.
What are the differences between one-sided and two-sided limits?
One-sided: Limit from left or right. Two-sided: Limit from both sides, must be equal for the limit to exist.
What are the differences between average and instantaneous rate of change?
Average: Slope of secant line. Instantaneous: Slope of tangent line.
What does a hole in the graph of a function indicate about its limit?
It indicates a removable discontinuity. The limit may exist even though the function is not defined at that point.
What does a vertical asymptote on the graph of a function tell us about its limits?
It indicates that the limit as x approaches that value is infinite or does not exist.
How can you identify a jump discontinuity from a graph?
The graph will have a sudden 'jump' in value at a particular x-value, with different one-sided limits.
What does the Squeeze Theorem state?
If $g(x) \leq f(x) \leq h(x)$ for all x near a, and $\lim_{x \to a} g(x) = \lim_{x \to a} h(x) = L$, then $\lim_{x \to a} f(x) = L$.
What does the Intermediate Value Theorem (IVT) state?
If f is continuous on [a, b] and k is any number between f(a) and f(b), then there exists at least one number c in [a, b] such that f(c) = k.