A reason you might want 00 to be something other than 0 or 1 As the number x increases through positive values, the numbers 1>x and 1 > (ln x) both approach zero. What happens to the number A reason you might want 0° to be something other than 0 or 1As the number x increases through positive values, the numbers1/x and 1/(In.x) both approach zero. What happens to the number1/Inx)fx) = (G)as x increases? Here are two ways to find out.a. Evaluate f for x = 10, 100, 1000, and so on as far as yourcalculator can reasonably go. What pattern do you see?b. Graph f in a variety of graphing windows, including win-dows that contain the origin. What do you see? Trace they-values along the graph. What do you find?

The given function is fx=1x1/lnx. (a) To Find: values of function for x=10,100,1000,... and find the…

Answered: A reason you might want 0° to be…

Advanced Engineering Mathematics

10th Edition

ISBN:9780470458365

Author:Erwin Kreyszig

Publisher:Erwin Kreyszig

Chapter2: Second-order Linear Odes

Section: Chapter Questions

Problem 1RQ

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A reason you might want 00 to be something other than 0 or 1 As the number x increases through positive values, the numbers 1>x and 1 > (ln x) both approach zero. What happens to the number

A reason you might want 0° to be something other than 0 or 1
As the number x increases through positive values, the numbers
1/x and 1/(In.x) both approach zero. What happens to the number
1/Inx)
fx) = (G)
as x increases? Here are two ways to find out.
a. Evaluate f for x = 10, 100, 1000, and so on as far as your
calculator can reasonably go. What pattern do you see?
b. Graph f in a variety of graphing windows, including win-
dows that contain the origin. What do you see? Trace the
y-values along the graph. What do you find?

Expert Solution

Step 1

The given function is $f (x) = {(\frac{1}{x})}^{1 / \ln x}$ .

(a) To Find: values of function for x=10,100,1000,... and find the pattern.

(b) To Plot: the graph of this function and write the observation.

Step 2

The given function is $f (x) = {(\frac{1}{x})}^{1 / \ln x}$ .

At $x = 10$ , $f (x) = 0.368$ .

At x=100, $f (x) = 0.368$ .

At x=1000, $f (x) = 0.368$ .

At x=10,000, $f (x) = 0.368$ .

At x=10,0000, $f (x) = 0.368$ .

Here we see that value of the function remain same as we increase x.

So, $f (x) \to 0.368 as x \to \infty$ .

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