MATH 1591 - Review of Chapter 1
1 Main Topics
1. Basic rules of limits.
2. How to use the direct substitution to find a limit.
3. How to use the factoring technique to find a limit.
4. How to use the rationalizing technique to find a limit.
5. How to use the Squeeze Theorem to find a limit.
6. How to use the important limit
lim
x→0
sin x
x= lim
x→0
sin cx
cx = lim
x→0
sin(xn)
xn= 1
to find a limit.
7. How to compute limits of piece-wise defined functions.
8. How to use the one-sided limits to prove that a limit does not exists.
9. The definition of continuity.
10. Properties of continuity.
11. How to find discontinuous points of a function.
12. How to use the intermediate value theorem to prove a function has a zero.
13. How to determine infinite limits.
14. How to find the vertical asymptotes.
15. How to find limits at infinity.
16. how to find the horizontal asymptotes.
17. the ε−δdefinition of a limit.
2 Review Exercises
Review Exercises of Chapter 1: All odd numbers from 11 to 47 plus 38.
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