Concept explainers
a.
the relationship between the vertical asymptotes of the graph of rational function and vertical asymptotes of the graphs representing the partial fractions of the decomposition.
a.
Answer to Problem 66E
The vertical asymptotes of the graph of rational function and vertical asymptotes of the graphs representing the partial fractions of the decomposition are same.
Explanation of Solution
Given information:
The function is given as
Concept used:
To find vertical asymptotes of a rational function, simply equate the denominator of rational function to 0 and then solve the equation.
Calculation: Finding the asymptotes of rational function
Here denominator is
So
Asymptotes of rational function are 0 and 4.
Finding the asymptotes of a partial fraction
Here the denominator is x , so
Finding the asymptotes of a partial fraction
Here the denominator is
So asymptotes of partial fraction are 0 and 4
Conclusion: The vertical asymptotes of the graph of rational function and vertical asymptotes of the graphs representing the partial fractions of the decomposition are same i.e. 0 and 4
b.
the relationship between the vertical asymptotes of the graph of rational function and vertical asymptotes of the graphs representing the partial fractions of the decomposition.
b.
Answer to Problem 66E
The vertical asymptotes of the graph of rational function and vertical asymptotes of the graphs representing the partial fractions of the decomposition are same.
Explanation of Solution
Given information: The function is given as
Concept used: To find vertical asymptotes of a rational function, simply equate the denominator of rational function to 0 and then solve the equation.
Calculation: Finding the asymptotes of rational function
Here denominator is
So
Asymptotes of rational function are 3 and -3.
Finding the asymptotes of a partial fraction
Here the denominator is
So
Finding the asymptotes of a partial fraction
Here the denominator is
So asymptotes of partial fraction are 3 and -3
Conclusion: The vertical asymptotes of the graph of rational function and vertical asymptotes of the graphs representing the partial fractions of the decomposition are same i.e. 3 and -3
Chapter 7 Solutions
EBK PRECALCULUS W/LIMITS
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