MA101: Single-Variable Calculus I

Upon the successful completion of this unit, you will be able to:

• define and calculate limits and one-sided limits;
• identify vertical asymptotes;
• define continuity and determine whether a function is continuous;
• state and apply the Intermediate Value Theorem;
• state the Squeeze Theorem, and use it to calculate limits;
• calculate limits at infinity and identify horizontal asymptotes;
• calculate limits of rational and radical functions;
• state the epsilon-delta definition of a limit, and use it in simple situations to show a limit exists;
• draw a diagram to explain the tangent-line problem;
• state several different versions of the limit definition of the derivative, and use multiple notations for the derivative;
• describe the derivative as a rate of change, and give some examples of its application, such as velocity; and
• calculate simple derivatives using the limit definition.