Quiz (The Limit of a Function)

(1) Estimate the limits, if they exist, by using a table of values to two decimal places:

    (a)         (b)     (c)
    
(2)  Sketch the graph of and Then identify the values of for which and exist given

    (a)     (b)
    
(3) Find so that the function satisfies

(4) Use the formal definition of a limit to show that

(5) Estimate the limits by using tables of values for

    (a)           (b)

Then using long division (or synthetic division if you know it) explain why one of the limits exists and the other does not.

(6) Consider the function Estimate by evaluating at -values near 0. Sketch the graph of

(7) Explain why does not exist.

(8) Evaluate the function for and Guess the value of Evaluate the function for and Guess again.

(9) The tabular approach is a convenient device for discussing limits informally, but if it is not used carefully, it can be misleading. For example, for let



    (a) Construct a table showing the value of and for and Based on this table what would you say about
    
    (b) Construct a table showing the value of and for Based on this table what would you say about
    
    (c) Based on your results in (a) and (b) what do you conclude about
     

• print this page
• pages linking here
• related pages