 # Rates, Sums, Limits, and Continuity

## Presentations

1. Trapezoid Rule (pdf)
2. Summation Notation (pdf)
3. Limits (pdf)
4. Continuity (pdf)

## Challenge Options

Many of the handouts have embedded challenge options

## Outline

— We will approximate the area under a curve using Riemann sums and summation notation. We will also use trapezoids to approximate the area.

— We will explore limits through approach statements, graphs, and algebra. We will predict function behavior with limits. We will also use limits to define continuity and see how continuity provides the basis for the Intermediate Value Theorem.

— We will apply our knowledge of rates of change to develop a method to approximate the velocity of an object at an instant. We will also explore local linearity concepts..

— Honors students, we will analyze the proofs of important trigonometric limits.

— We will complete the development of Riemann sums and use Desmos to investigate using left endpoint, right endpoint, and midpoint rectangles to approximate area under a curve. ## Goals

• Approximate the area under a curve using Riemann sums and summation notation.
• Predict function behavior with limits.
• Formally define continuity.
• Discuss local linearity.
• Approximate the velocity of an object at an instant.