Number & Quantity and Algebra

Chapter 1

Number & Quantity and Algebra

Course: Praxis Mathematics 5165
Subject: Praxis Study Companion Mathematics 5165
Chapter: Functions And Calculus Of Praxis Study Companion Mathematics 5165

Understands the Meaning of a Limit and How to Calculate Limits

A limit describes what value a function approaches as the input approaches a specific number, even if the function is not defined at that number. Limits capture local behavior near a point and are the foundation of continuity, derivatives, and many modeling ideas in calculus. The notation lim⁡x→cf(x) means “the value that f(x) gets arbitrarily close to as x gets arbitrarily close to c.” A limit can exist even if f(c) does not exist, and a limit can fail to exist even if f(c) exists.

Solves Limits Using Limit Laws

Limit laws allow you to compute complicated limits by breaking them into simpler parts, provided the individual limits exist and the operations are valid. The key idea is that limits preserve algebraic structure when the function behavior is well-behaved at the approach point.