Essential Understanding 1.2

Essential Understanding 1.2 Students will understand that continuity is a key property of functions that is defined using limits.

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As you'll see later in the year, all of the useful calculus ideas will require continuous functions. We find ourselves in a situation similar to learning limits. By that I mean, while determining continuity rarely provides anything useful itself, useful things like derivatives do require continuity, so we need to learn about continuity.

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Learning Objective 1.2A Students will be able to analyze functions for intervals of continuity or points of discontinuity.

Essential Knowledge 1.2A1 Students will know that a function f is continuous at x = c provided that f(c) exists, exists, and

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Essential Knowledge 1.2A2 Students will know that polynomial, rational, power, exponential, logarithmic, and trigonometric functions are continuous at all points in their domains.

Essential Knowledge 1.2A3 Students will know that types of discontinuities include removable discontinuities, jump discontinuities, and discontinuities due to vertical asymptotes.

Learning Objective 1.2B Students will be able to determine the applicability of important calculus theorems using continuity.

Essential Knowledge 1.2B1 Students will know that continuity is an essential condition for theorems such as the Intermediate Value Theorem, the Extreme Value Theorem, and the Mean Value Theorem.