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calculus:resources:calculus_videos:chapter1

## The Limit of a Function

Section 1.5 in Stewart's Calculus.

Preclass Learning Objectives:

• The limit at an x-value describes the y-value the function “approaches” at that x-value.
• Graphical intuition for limits.
• Two-sided limits depend on both one-sided limits.

## Tangents, Derivatives, and Rates of Change

Section 1.4/2.1 in Stewart's Calculus.

Preclass Learning Objectives:

• A rate of change describes how one quantity changes in relation to another quantity.
• Rate of change can result from averaging over an interval or finding a limit of averages approaching a single point.
• Tangent lines result from the limit of secant lines.
• A derivative is an instantaneous rate of change.

## Limit Laws

Section 1.6 in Stewart's Calculus.

Preclass Learning Objectives:

• Algebraic limit laws.
• When direct substitution isn't allowable in calculating a limit try simplification, conjugation, or squeezing the function.

## Continuity

Section 1.8 in Stewart's Calculus.

Preclass Learning Objectives:

• Graphical intuition of continuity.
• Where limits align with actual values, a function is continuous.
• Types of discontinuities.
• Algebraic limit laws.
• Continuous functions cannot jump (Intermediate Value Theorem).