Unit 4 - Introduction to Calculus

Unit 4 Review Problems 

This document provides a good source of problems to solve in preparation for Unit 4. You should also study for the Final Exam by re-solving problems from class, past quizzes, online homework problems, as well as the review problem sets for Unit 1, Unit 2, Unit 3 and Unit 4. Answers to the problems in this document are provided at the end. On a test, you will earn most of the available points for a given problem by carefully showing the steps taken to reach your answer, rather than for the final answer itself.

Unit 4 Learning Objectives:

• Evaluate limits numerically, graphically, and algebraically

• Identify 'holes' in the graph of a rational function by evaluating a limit

• Evaluate infinite limits graphically and make the connection between infinite limits and vertical asymptotes

• Reproduce the reasoning used to show where the tangent function has vertical asymptotes to conclude where, for example, a reciprocal function has a vertical asymptote

• Evaluate limits at infinity graphically and make the connection between limits at infinity and horizontal asymptotes

• Describe the behavior of a piecewise function using one-sided limits

• Compute an average rate of change, given a function defined by a graph, an equation, or a table of values

• Draw the secant line connecting two points on a curve

• Interpret the slope of a secant line as an average rate of change

• Form and simplify a difference quotient representing the slope of a secant line connecting two arbitrary points on a curve

• Use proper units for rates of change in applied problems

• Calculate distance traveled as a rate of change multiplied by time elapsed