This

**preview**shows half of the first page. to view the full**2 pages of the document.**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

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