In a certain city there is a river running through the middle of the city. There are three islands and seven bridges as shown in the figure below.
It is possible to take a walk through this town, starting on the North Bank, crossing each bridge once (and only once) and ending
A. on the South Bank.
B. back on the North Bank.
C. on island B.
D. on island C.
E. none of these
Answer: D
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Use the precise definition of a limit to prove the limit. Specify a relationship between ? and ? that guarantees the limit exists.
= 
A. ? = min
; Let ? > 0 and assume 0 < 
< ?. Then 
= 
= 
= ?. That is, for any ? > 0, 
< = ? whenever 0 < 
< ?, provided 0 < ? ? 
. Therefore, 
= 
.
B. ? = min
; Let ? > 0 and assume 0 < 
< ?. Then 
= 
= 
= ?. That is, for any ? > 0, 
= ? whenever 0 <
< ?, provided 0 < ? ? 
. Therefore, 
= 
.
C. ? = min
; Let ? > 0 and assume 0 < 
< ?. Then 
= 
< 
= ?. That is, for any ? > 0, 
< ? whenever 0 < 
< ?, provided 0 < ? ? 
. Therefore, 
= 
.
D. ? = min
; Let ? > 0 and assume 0 < 
< ?. Then 
= 
< 
= ?. That is, for any ? > 0, 
< ? whenever 0 < 
< ?, provided 0 < ? ?
. Therefore, 
= 
.
Solve the problem.In 1980, the population of a city was 6.8 million. By 1992 the population had grown to 9.5 million. Find the average rate of change in population from 1980 to 1992..
A. 
million per year
B. 
million per year
C. 
million per year
D. 
million per year
Graph the equation as a solid line. Graph the inverse relation as a dashed line on the same axes by reflecting across the line y = x.x = 3
A. 
B. 
C. 
D. 
Solve the problem.Find two consecutive positive integers such that the square of the larger integer added to seven times the smaller integer is equal to 253.
A. 21, 22 B. No such integers exist. C. 12, 13 D. -21, -20