Covers sections 2.1-2.5

(Chapter 1 is review - not on test 1) 

To study for the test: 

1) Know all the concepts on this review sheet. 

2) Do Old Test 1 

3) Study the posted HW problems for the sections on the test. 

Section 2.1 - Idea of Limits

• Know that the average rate of change of f(x) on the interval [a, b] is:

• Know that the instantaneous rate of change of f(x) at x = a is:

Section 2.2 - Definition of Limits

• Know that the limit exists at x = a if 

      = L

• Be able to sketch piecewise functions. 

• Be able to use the "table" feature of the calculator to determine a limit.
• Know one-sided limits:

           

           

Section 2.3 - Techniques for computing limits

Limit Rules 

  1)  

  2)  

  3)  

  4)  

  5)  

  6)  

  7)  

  8)

 

  9) 

For Polynomials, P(x) 

Quotients of functions

          If

 

          then cancel common factors and then take the limit.

Squeeze Theorem 

      If       and and 

      then

Exponentials and Logarithms 

Know how to compute the limit of:
    |f(x)|/f(x)

Section 2.4 - Infinite Limits

• Know what each of the following look like on a graph:

         (is a V.A., vertical asymptote) 

       (is a V.A., vertical asymptote)

Theorem (**)

Section 2.5 - Limits at Infinity

      (is a H.A., horizontal asymptote) 

      (is a H.A., horizontal asymptote)

For Polynomials, P(x) 

Theorem (**) 

For rational functions look at the leading term over the leading term, reduce and then take the limit.