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, 
= 
.
Answer: D
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A. Does not exist B. 0 C. 3 D. -3
Write as a proportion.81 is to 72 as 9 is to 8.
A. 
= 
B. 
= 
C. 
= 
D. 
= 
Solve the problem.To obtain a certain shade of paint, Peter mixed 
of white paint with 
of brown and 
of blue paint. How much paint did he have?
A. 
gal
B. 
gal
C. 8
gal
D. 1
gal
Solve the equation.x2 - 2x = 24
A. 4, -6 B. -4, 6 C. -4, -6 D. 4, 6