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Unformatted text preview: Answer Guide 2 Math 408C: Unique Numbers 56975, 56980, and 56985 Tuesday, September 8, 2009 Homework problems Section 2.2 8. Examining the given graph, we see that: (a) lim x ! 2 R ( x ) = &amp;1 . (b) lim x ! 5 R ( x ) = + 1 . (c) lim x ! 3 &amp; R ( x ) = &amp;1 . (d) lim x ! 3+ R ( x ) = + 1 : 12. Examining the graph below, we see that lim x ! a f ( x ) exists for all a except a = &amp; 1 and a = +1 .54321 1 2 3 4 52 2 4 6 8 10 x y 38. (a) With h ( x ) = tan x &amp; x x 3 , we use a calculator to compute that h (0 : 005) = 0 : 333 34 h (1) = 0 : 557 41 ; h (0 : 5) = 0 : 370 42 ; h (0 : 1) = 0 : 334 67 ; h (0 : 05) = 0 : 333 67 ; h (0 : 01) = 0 : 333 35 ; h (0 : 005) = 0 : 333 34 : (b) The brief numerical experiment above suggests that lim x ! h ( x ) = 1 = 3 , which is correct. 1 (c) However, if you continue the numerical experiment and ask your calculator to eval uate h ( x ) for successively smaller values of x , it will eventually give false values. For example, my computer claims that h (1 : &amp; 10 &amp; 14 ) = 0 : , which is wrong. Numerical experiments are often unreliable when faced with limits of the form &amp; = . Later in the course, we will learn techniques to correctly evaluate limits like this....
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This note was uploaded on 02/09/2010 for the course M 408c taught by Professor Mcadam during the Fall '06 term at University of Texas at Austin.
 Fall '06
 McAdam
 Math, Calculus

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