Students demonstrate knowledge of both the formal definition and the graphical interpretation of limit of values of functions. This knowledge includes one-sided limits, infinite limits, and limits at infinity. Students know the definition of convergence and divergence of a function as the domain variable approaches either a number or infinity:

1.1 Students prove and use theorems evaluating the limits of sums, products, quotients, and composition of functions.

1.2 Students use graphical calculators to verify and estimate limits.

1.3 Students prove and use special limits, such as the limits of (sin(x))/x and (1-cos(x))/x as x tends to 0.

Unit 1: Limits & Continuity

This unit focuses on limits and continuity. Students calculate limits graphically, numerically and analytically. Students determine the continuity of a function and apply the intermediate value and extreme value theorem.

Limits

Estimating Graphically & Numerically

Evaluating Analytically

One-Sided Limits

Infinite Limits & Limits at Infinity

Vertical & Horizontal Asymptotes

Definition of Continuity

Continuity at a Point

Continuity on an Open & Closed Interval

Intermediate Value Theorem

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