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MATH 1591: Limits Review - Chapter 1 - Prof. Wei-Jiu Liu, Study notes of Calculus

An overview of the main topics covered in chapter 1 of math 1591, including rules of limits, techniques for finding limits, and properties of continuity. It also includes a list of review exercises for odd number problems from 11 to 47 and 38.

Typology: Study notes

Pre 2010

Uploaded on 08/18/2009

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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
x0
sin x
x= lim
x0
sin cx
cx = lim
x0
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 εδdefinition of a limit.
2 Review Exercises
Review Exercises of Chapter 1: All odd numbers from 11 to 47 plus 38.
1

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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

xlim→ 0 sinx^ x= lim x→ 0 sincx^ cx = lim x→ 0 sin(x

n) xn^ = 1 to find a limit.

  1. How to compute limits of piece-wise defined functions.
  2. How to use the one-sided limits to prove that a limit does not exists.
  3. The definition of continuity.
  4. Properties of continuity.
  5. How to find discontinuous points of a function.
  6. How to use the intermediate value theorem to prove a function has a zero.
  7. How to determine infinite limits.
  8. How to find the vertical asymptotes.
  9. How to find limits at infinity.
  10. how to find the horizontal asymptotes.
  11. the ε − δ definition of a limit.

2 Review Exercises

Review Exercises of Chapter 1: All odd numbers from 11 to 47 plus 38.