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Theory and ApplicationsThe function (Continuation of
Chapter 4, Problem 90E(choose chapter or problem)
Problem 90E
Theory and Applications
The function (Continuation of Exercise 89.)
a. Graph . Howdo you account for the gaps in the graph? How wide are the gaps?
b. Now graph ƒ on the interval . The function is not defined at , but the graph has no break at this point. What is going on? What value does the graph appear to give for ƒ at ?(Hint: Use l’Hôpital’s Rule to find lim ƒ as
c. Continuing with the graphs in part (b), find max ƒ and min ƒ as accurately as you can and estimate the values of x at which they are taken on.
Reference: Exercise 89
The continuous extension of
a. Graph on the interval . What value would you assign to ƒ to make it continuous at
b. Verify your conclusion in part (a) by finding with l’Hôpital’s Rule.
c. Returning to the graph, estimate the maximum value of ƒ on . About where is max ƒ taken on?
d. Sharpen your estimate in part (c) by graphing in the same window to see where its graph crosses the x-axis. To simplify your work, you might want to delete the exponential factor from the expression for and graph just the factor that has a zero.
Questions & Answers
QUESTION:
Problem 90E
Theory and Applications
The function (Continuation of Exercise 89.)
a. Graph . Howdo you account for the gaps in the graph? How wide are the gaps?
b. Now graph ƒ on the interval . The function is not defined at , but the graph has no break at this point. What is going on? What value does the graph appear to give for ƒ at ?(Hint: Use l’Hôpital’s Rule to find lim ƒ as
c. Continuing with the graphs in part (b), find max ƒ and min ƒ as accurately as you can and estimate the values of x at which they are taken on.
Reference: Exercise 89
The continuous extension of
a. Graph on the interval . What value would you assign to ƒ to make it continuous at
b. Verify your conclusion in part (a) by finding with l’Hôpital’s Rule.
c. Returning to the graph, estimate the maximum value of ƒ on . About where is max ƒ taken on?
d. Sharpen your estimate in part (c) by graphing in the same window to see where its graph crosses the x-axis. To simplify your work, you might want to delete the exponential factor from the expression for and graph just the factor that has a zero.
ANSWER:
SOLUTION:
Step 1:
In this question we have to graph . And account for the gaps in the graphs. Also find the maximum and minimum value of .
