As the number x increases through positive values, the numbers 1/x and 1/(ln x) both approach zero. What happens to the number ƒ(x) = (1/ x)^(1/lnx) as x increases? Here are two ways to find out. a. Evaluate ƒ for x = 10, 100, 1000, and so on as far as your calculator can reasonably go. What pattern do you see? b. Graph ƒ in a variety of graphing windows, including windows that contain the origin. What do you see? Trace the y-values along the graph. What do you find?
As the number x increases through positive values, the numbers 1/x and 1/(ln x) both approach zero. What happens to the number ƒ(x) = (1/ x)^(1/lnx) as x increases? Here are two ways to find out. a. Evaluate ƒ for x = 10, 100, 1000, and so on as far as your calculator can reasonably go. What pattern do you see? b. Graph ƒ in a variety of graphing windows, including windows that contain the origin. What do you see? Trace the y-values along the graph. What do you find?
Linear Algebra: A Modern Introduction
4th Edition
ISBN:9781285463247
Author:David Poole
Publisher:David Poole
Chapter6: Vector Spaces
Section6.7: Applications
Problem 14EQ
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As the number x increases through positive values, the numbers 1/x and 1/(ln x) both approach zero. What happens to the number ƒ(x) = (1/ x)^(1/lnx) as x increases? Here are two ways to find out. a. Evaluate ƒ for x = 10, 100, 1000, and so on as far as your calculator can reasonably go. What pattern do you see? b. Graph ƒ in a variety of graphing windows, including windows that contain the origin. What do you see? Trace the y-values along the graph. What do you find?
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