## Week 26

Reference: Stewart page xvi, Handout, Stewart Appendix A, Stewart 1.4

Keywords: Symbolic logic, universal and existential quantifiers, implication, truth tables, limit of a function, epsilon-delta definition

Learning Objectives: The student will be able to:

• Translate English statements involving "for all" or "for every", "there exists", and "if ... then" or "implies" into mathematical notation, and vice versa
• Distinguish the meanings of phrases such as the following, and express them in mathematical notation:
• "For every epsilon there is a delta such that ... "
• "There is a delta such that for every epsilon ... "
• "There exist an epsilon and a delta such that ... "
• Solve simple inequalities, especially inequalities involving absolute values
• State the precise definition of a limit

26.R Limits II

Reference: Stewart 1.4, 1.3, Appendix F

Keywords: Limit of a function, one-sided limits, epsilon-delta definition, limit laws

Learning Objectives: The student will be able to:

• Explain the definition of a limit graphically
• Use the definition of a limit to prove limits in simple cases
• Use the definition of a limit to prove some of the limit laws, such as "the limit of sum is the sum of the limits"