10. (4 pts) Evaluate the limit if it exists. If it does not exist, explain whether it is co, -co, or neither. 2x+12 lim x-6x+6| Solution First, work on the right-sided limit: Suppose x-6+. Then x>-6, so x+6>0. Therefore, |x+6|=x+6 (from the definition of the absolute value function). Hence, lim = 2x+12 lim 2(x+6) = lim 2=2 x-6x+6x-6+ x+6 x-6+ Reasoning: (0, 0.5, 1) Answer for the right-sided Limit: (0, 0.5) Next, work on the left-sided limit. Suppose x-6. Then x<-6, so x+6<0. Therefore, |x+6|==(x+6) (from the definition of the absolute value function). Hence, lim 2x+12 lim 2(x+6) Reasoning: (0, 0.5, 1) lim (-2)--2 x-6x+6x-6¯ −(x+6) x→−6¯ Answer for the left-sided Limit: (0,0.5) Conclusion: (0, 0.5, 1) Since the two one-sided limits are different, we conclude that the limit, lim 2x+12 does not exist x-6x+6|' and is neither co nor-00.
10. (4 pts) Evaluate the limit if it exists. If it does not exist, explain whether it is co, -co, or neither. 2x+12 lim x-6x+6| Solution First, work on the right-sided limit: Suppose x-6+. Then x>-6, so x+6>0. Therefore, |x+6|=x+6 (from the definition of the absolute value function). Hence, lim = 2x+12 lim 2(x+6) = lim 2=2 x-6x+6x-6+ x+6 x-6+ Reasoning: (0, 0.5, 1) Answer for the right-sided Limit: (0, 0.5) Next, work on the left-sided limit. Suppose x-6. Then x<-6, so x+6<0. Therefore, |x+6|==(x+6) (from the definition of the absolute value function). Hence, lim 2x+12 lim 2(x+6) Reasoning: (0, 0.5, 1) lim (-2)--2 x-6x+6x-6¯ −(x+6) x→−6¯ Answer for the left-sided Limit: (0,0.5) Conclusion: (0, 0.5, 1) Since the two one-sided limits are different, we conclude that the limit, lim 2x+12 does not exist x-6x+6|' and is neither co nor-00.
Big Ideas Math A Bridge To Success Algebra 1: Student Edition 2015
1st Edition
ISBN:9781680331141
Author:HOUGHTON MIFFLIN HARCOURT
Publisher:HOUGHTON MIFFLIN HARCOURT
Chapter4: Writing Linear Equations
Section: Chapter Questions
Problem 7CA
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Transcribed Image Text:10. (4 pts) Evaluate the limit if it exists. If it does not exist, explain whether it is co, -co, or neither.
2x+12
lim
x-6x+6|
Solution
First, work on the right-sided limit: Suppose x-6+. Then x>-6, so x+6>0. Therefore,
|x+6|=x+6 (from the definition of the absolute value function). Hence,
lim
=
2x+12
lim 2(x+6)
= lim 2=2
x-6x+6x-6+ x+6 x-6+
Reasoning: (0, 0.5, 1)
Answer for the right-sided Limit: (0, 0.5)
Next, work on the left-sided limit. Suppose x-6. Then x<-6, so x+6<0. Therefore,
|x+6|==(x+6) (from the definition of the absolute value function). Hence,
lim
2x+12
lim
2(x+6)
Reasoning: (0, 0.5, 1)
lim (-2)--2
x-6x+6x-6¯ −(x+6) x→−6¯
Answer for the left-sided Limit: (0,0.5)
Conclusion: (0, 0.5, 1)
Since the two one-sided limits are different, we conclude that the limit, lim
2x+12
does not exist
x-6x+6|'
and is neither co nor-00.
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