Precalculus with Limits: A Graphing Approach
7th Edition
ISBN: 9781305071711
Author: Ron Larson
Publisher: Brooks/Cole
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Question
Chapter 11, Problem 33RE
(a)
To determine
To graph:
The limit value of the following functions:
limx→3 x−3x2−9
(a)
Expert Solution
Explanation of Solution
Given information:
limx→3 x−3x2−9
Graph:
Interpretation:
The given function is:
limx→3 x−3x2−9
The graph of the limit value at x=3 is drawn as above.
From the graph of the limit function limx→3 x−3x2−9 converges to single bounded value as it approaches 3 both from left and right side.
(b)
To determine
To calculate:
The limit value of the following functions numerically:
limx→3 x−3x2−9
(b)
Expert Solution
Answer to Problem 33RE
The limit value of limx→3 x−3x2−9 is 16 .
Explanation of Solution
Given information:
limx→3 x−3x2−9
Calculation:
The given function is:
limx→3 x−3x2−9
The limit of the function as x→3 is calculated as:
limx→3 x−3x2−9=limx→3 (x−3)x2−32limx→3 x−3x2−9=limx→3 (x−3)(x−3)(x+3)limx→3 x−3x2−9=limx→3 1(x+3)limx→3 x−3x2−9=1(3+3) [∵x=3]limx→3 x−3x2−9=16limx→3 x−3x2−9=0.167
Hence, the limiting value is 16 .
Chapter 11 Solutions
Precalculus with Limits: A Graphing Approach
Ch. 11.1 - Prob. 1ECh. 11.1 - Prob. 2ECh. 11.1 - Prob. 3ECh. 11.1 - Prob. 4ECh. 11.1 - Prob. 5ECh. 11.1 - Prob. 6ECh. 11.1 - Prob. 7ECh. 11.1 - Prob. 8ECh. 11.1 - Prob. 9ECh. 11.1 - Prob. 10E
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