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6 Pages

### lab3

Course: MATH 114, Fall 2009
School: Wisc Eau Claire
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Word Count: 395

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114 Math Fall 2005 Lab 3 We can modify the definitions on page 119 in various ways. For example: The definition of the assertion xa+ lim f (x) = is that for every positive number B there is a positive such that f (x) will exceed B whenever x is between a and a + . Here is a picture for this definition. Note y &gt; B when x is between a and a + . B y=f(x) a d By making similar modifications, we can come...

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114 Math Fall 2005 Lab 3 We can modify the definitions on page 119 in various ways. For example: The definition of the assertion xa+ lim f (x) = is that for every positive number B there is a positive such that f (x) will exceed B whenever x is between a and a + . Here is a picture for this definition. Note y > B when x is between a and a + . B y=f(x) a d By making similar modifications, we can come up with definitions for the following assertions: lim f (x) = lim f (x) = - lim f (x) = - lim f (x) = lim f (x) = L lim f (x) = - lim f (x) = L xa- xa+ xa- x x- x lim f (x) = x lim f (x) = - x- x- If we consider f (x) = verify this with Maple by limit(3/(x-1),x=1,right); We could obtain a plot with Maple by plot(3/(x-1),x=0..2,y=-50..50,discont=true); 3 then we know that lim f (x) = . We can x1+ x-1 40 20 y 0 0 0.5 1 x -20 1.5 2 -40 In view of the definition of the limit, it is fair to ask this quantitative question: How close does x need to be to 1 to be sure that f (x) will be than greater 10,000? This amounts to solving the inequality f (x) > 10, 000. We can solve this with Maple as follows: solve(3/(x-1)>10000); solve(3/(x-1)>10000.); We see that = 0.003 is sufficiently small. Lab Report (due Sept. 29) Names: Lab Time: For each of the following limits carefully state the definition and provide a sketch, as described on the first page. Then answer the quantitative question. Use Maple as a tool as you see fit. Explain how you come to your conclusion. 1. lim+ f (x) = - xa Since lim + 8 = -, how close to 2 does x need to be to be sure x2 2 - x that f (x) will be less...

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#file=swbz_15-350lc.txt dt=0.4 tstart=32.150 tstop=92.950#t90 dt90 t50 dt50 rt90 drt90 rt50 drt50 rt45 drt45 tav dtav tmax dtmax trise dtrise tfall dtfall cts cts_err pk_rate dpk_rate band 39.600 2.640 18.800 1.311 30.800
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