Angles, Radian Measure, and Unit Circle.

Duration of Unit: 15 days

Missouri Learning Standards/ Essential Learning Outcomes

Section 2.1

2.1.1 Describe the tangent problem and how it led to the idea of a derivative.
2.1.2 Explain how the idea of a limit is involved in solving the tangent problem.
2.1.3 Recognize a tangent to a curve at a point as the limit of secant lines.
2.1.4 Identify instantaneous velocity as the limit of average velocity over a small time interval.
2.1.5 Describe the area problem and how it was solved by the integral.
2.1.6 Explain how the idea of a limit is involved in solving the area problem.
2.1.7 Recognize how the ideas of limit, derivative, and integral led to the studies of infinite series and multivariable calculus.

Section 2.2

2.2.1 Using correct notation, describe the limit of a function.
2.2.2 Use a table of values to estimate the limit of a function or to identify when the limit does not exist.
2.2.3 Use a graph to estimate the limit of a function or to identify when the limit does not exist.
2.2.4 Define one-sided limits and provide examples.
2.2.5 Explain the relationship between one-sided and two-sided limits.
2.2.6 Using correct notation, describe an infinite limit.
2.2.7 Define a vertical asymptote.

Section 2.3

2.3.1 Recognize the basic limit laws.
2.3.2 Use the limit laws to evaluate the limit of a function.
2.3.3 Evaluate the limit of a function by factoring.
2.3.4 Use the limit laws to evaluate the limit of a polynomial or rational function.
2.3.5 Evaluate the limit of a function by factoring or by using conjugates.
2.3.6 Evaluate the limit of a function by using the squeeze theorem.

Section 2.4

2.4.1 Explain the three conditions for continuity at a point.
2.4.2 Describe three kinds of discontinuities.
2.4.3 Define continuity on an interval.
2.4.4 State the theorem for limits of composite functions.
2.4.5 Provide an example of the intermediate value theorem.

Section 2.5

2.5.1 Describe the epsilon-delta definition of a limit.
2.5.2 Apply the epsilon-delta definition to find the limit of a function.
2.5.3 Describe the epsilon-delta definitions of one-sided limits and infinite limits.
2.5.4 Use the epsilon-delta definition to prove the limit laws.

Big Idea of the Unit:
What are limits? How do we find them?

Specific Assessment Evidence:

The assessment will be a paper & pencil test. It could be comprised of multiple-choice, matching, and/or fill in the blank. Most of the points in this assessment will come from the multi-step problems.

Math Resources
Link to the Missouri Learning Standards
DESE Math Curriculum and Instruction Homepage