Rates, Sums, Limits, and Continuity

Handouts

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.

— 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.
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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.