Continuity and One-Sided limits

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Continuity and One-Sided limits Rizzi – Calc BC

Continuity – A simple Concept Baby definition: No holes or jumps in the graph Can draw graph without picking up pencil

Continuity – Let’s Make it Harder Than it Has to Be A function f is continuous at point c when these three conditions are met: 1. 2. 3. f(c) is defined

One-Sided Limits

Types of Discontinuity Removable Discontinuity: Limit on both sides of the discontinuity are the same Nonremovable Discontinuity: Limit on both sides of the discontinuity are not the same

Example Find the x-values where f is not continuous. Classify the discontinuities as removable or nonremovable.

Intermediate Value THeorem I’m traveling to Florida. Assuming I take I-75 to get there, can I make it to Florida without passing through Ohio?

Intermediate Value Theorem (IVT) The IVT states that if I have a closed interval where my endpoints are not equal, then I should pass through every output value to get from the left endpoint to the right endpoint.

IVT In Fancier Terms If f is continuous on the closed interval [a, b], f(a) ≠ f(b), and k is any number between f(a) and f(b), then there is at least one number c in [a, b] such that f(c) = k

Applying the IVT Use the IVT to show that f has a zero in the interval [1, 2]

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