{[ promptMessage ]}

Bookmark it

{[ promptMessage ]}

AnswerKey2 - Answer Guide 2 Math 408C Unique Numbers 56975...

Info iconThis preview shows pages 1–3. Sign up to view the full content.

View Full Document Right Arrow Icon
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 ) = °1 . (b) lim x ! 5 R ( x ) = + 1 . (c) lim x ! 3 ° R ( x ) = °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 = ° 1 and a = +1 . -5 -4 -3 -2 -1 1 2 3 4 5 -2 2 4 6 8 10 x y 38. (a) With h ( x ) = tan x ° 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 ! 0 h ( x ) = 1 = 3 , which is correct. 1
Background image of page 1

Info iconThis preview has intentionally blurred sections. Sign up to view the full version.

View Full Document Right Arrow Icon
(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 : 0 ± 10 ° 14 ) = 0 : 0 , which is wrong. Numerical experiments are often unreliable when faced with limits of the form ° 0 = 0 ±. Later in the course, we will learn techniques to correctly evaluate limits like this. The point of this exercise is not that computers are unreliable. They aren°t. But we do need critical thinking skills and some knowledge of calculus to know when we can ± and can°t ± trust what they tell us.
Background image of page 2
Image of page 3
This is the end of the preview. Sign up to access the rest of the document.

{[ snackBarMessage ]}