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Chapter 1

MATH 3A Chapter 1: Math3ALecture1

Department
Mathematics
Course Code
MATH 3A
Professor
Kelz
Chapter
1

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Math3A is â€¦
â€¢ Not Calc AB
â€¢ Not a course which emphasizes computation
â€¢ A course which will emphasize definitions, rules, theorems,
applications, and concepts
â€¢ A course which will prepare you for Math3B
Today we will discuss
â€¢ Sets of real numbers
â€¢ Functions of a real variable
â€¢ Limits
â€¢ What to expect from limit computations
Definition
Real numbers and the "typical sets of real numbers:
Definition
Domain, codomain, and rage of a function:
f: Aâ€”B
Examples of familiar functions:
What is algebraically equivalent to x2 + 5x + 6x + 2?
What are the domain and range of x2 + 5x + 6x + 2?
Let f : (a, b) âˆ’â†’ R and a < x0 < b.We say that the limit as x
approaches x0 from the left existsand is equal to L if for all Îµ > 0,
there exists a Î´ > 0 so thatwhenever 0 < x0 âˆ’ x < Î´ we have
|f(x) âˆ’ L| < Îµ.
Similarly, we say that the limit as x approaches x0 from theright
exists and is equal to R if for all Îµ > 0, there exists a Î´ > 0so that
whenever 0 < x âˆ’ x0 < Î´ we have |f(x) âˆ’ R| < Îµ.
How to conceptualize limits graphically
How to conceptualize limits algebraically