Unit 1 - Introduction to Calculus (18 Hours)
Unit Description and Learning Goal:
In this unit, students will then deal with rates of change problems and the limit concept. While the concept of a limit involves getting close to a value but never getting to the value, often the limit of a function can be determined by substituting the value of interest for the variable in the function. Students will work with several examples of this concept. To this point in the course students have been given a fixed point and have been asked to find the tangent slope at that value, in this section of the unit students will determine a tangent slope function similar to what they had done with a secant slope function.
By the end of the unit, you will be able to:
- simplify radical expressions
- use limits to determine the slope and the equation of the tangent to a graph.
- Pose problems and formulate hypotheses regarding rates of change
- Calculate and interpret the average and instantaneous rate of change and relate these values to slopes of secants and tangents.
- understand and evaluate limits using appropriate properties
- Examine continuous functions and use limits to explain why a function is discontinuous.