compare-the-functions-fxx01-and-gxln-x-by-graphing-both-f-and-g-in-several-viewing-rectangles-when-d

Name: compare the functions fxx01 and gxln x by graphing both f and g in several viewing rectangles when d
Uploaded: 2019-06-27
Duration: 2 min 20 s
Channel: Numerade
Description: Compare the functions $f(x)=x^{0.1}$ and $g(x)=\ln x$ by graphing both $f$ and $g$ in several viewing rectangles. When does the graph of $f$ finally surpass the graph of $g ?$

Question

Compare the functions $f(x)=x^{0.1}$ and $g(x)=\ln x$ by graphing both $f$ and $g$ in several viewing rectangles. When does the graph of $f$ finally surpass the graph of $g ?$

Carlos Pinilla · Accepted Answer

in these rip We&#x27;re off year degree percents eggs. The power of zero point one was O R. As you can see well are rough, But, uh, our approximation is like saying that that it is the line. Well, why equals one? That is true because, uh and he bought any point. The 40 is one so sort of dysfunction. You&#x27;re gonna be very approximate that line. Also, as you can see, they have this local. That function is very reasonable. Well, what role or even Lisa is, uh, is slowly increasing fortune. But all these bonus also was on you as it got you here. Follow you. 00 t. Like their own or all three. Not the only way we&#x27;ll fix becomes every year the mixed lee she won, But far beyond there this slope here. So we&#x27;re, uh, what this means in terms of differential. Calculus is taking day. They&#x27;re ready. Is that will be It&#x27;s more than others. Look, these were Well, it&#x27;s for some point for being there, But they&#x27;re right

Heather Zimmers · Answer

for this problem. We want to compare the graphs of F of X equals X to the 10th Power and G of X equals E to the X power. So we type both of those into the graphing calculator. We&#x27;re going to look at them using several different viewing windows and figure out the point of intersection when the exponential graph finally surpasses the polynomial graph. So I&#x27;m going to start with just a standard with viewing window negative 10 to 10. So go to zoom six. So we see the blue one is X to the 10th and we see the red one is y equals e to the X. So we can see that in this area right here. The blue one is higher than the red one. So the exponential graph has not surpassed the polynomial yet. Now we can change our window dimensions. Perhaps we can go a little higher with her y values. No, we go up to 1000. Take a look at that. We can see that the polynomial graph is still quite a bit higher than the exponential graph. So let&#x27;s make a few more changes. Maybe we go out to X equals 20 and perhaps we go all the way up to 10 to the eighth power. Well, the polynomial is still greater than the exponential graph, so let&#x27;s go out a little further. Let&#x27;s go out to X equals 50 and let&#x27;s go all the way up to why equals 10 to the 16th power. Okay, now we&#x27;ve seen a change. So we see a point of intersection. We see the point where the exponential graph surpasses the polynomial graph. And let&#x27;s find that point of intersection so we can go to the calculate menu. We can choose number five Intersect. Put the cursor on the first curve, press enter, put the cursor on the second curve, press enter and then move the cursor closer to the intersection. Point press. Enter and we get the intersection point, as is at about X, equals 35.8. And that&#x27;s at a Y value of 3.4 times 10 to the 15th Power

Amrita Bhasin · Answer

this question asked us to graph F N g in the same viewing window, and it says, When does the graph of GE surpassed a graph of F? The answer is at the point of intersection using a calculator, you can see if the X point of interception is approximately 35.8. At this point, the X coordinate of the point of intersection is when Jesus

Ankit Gupta · Answer

According to the question we need to compare the graph off DX equals X square. With the graph off effects equals X squared. Here we have the graph off. If X equals X square in part A, we have to consider if is between zero and one, then DX shrinks. That is G X equals X square shrinks. So all our accident lose in the graph are multiplied by route over off a. There is their route. A is less than one. So our graph we&#x27;ll become like this. G X equals X squared on in five B if is greater than one, then on graph or function, DX equals X square expense that is G X equals Rubio Overall e x whole square There route over off a is greater than one expense because eat off the X ex points are multiplied by road over off a which is greater than one. So a graph will become like this. So this is the graph for five function. DX equals X squared. There is good in one. So we compared all the three graphs where our graph shrinks. If is between zero and one on our graph expense, then is between a is greater than one

Heather Zimmers · Answer

in this problem, we&#x27;re going to use a graphing calculator to compare the functions f of X equals X to the fifth Power and G of X equals five to the X power. So we type those into our y equals menu, and what we want to do is look at them using several different viewing wreck rectangles, and then we&#x27;re gonna find the points of intersection. And so, for starters, for a good viewing with rectangle, I&#x27;m going to start with Zoom decimal, which is choice number four, and we can see that the red one is the five to the X power and the blue one is the X to the fifth power. Okay, so the five to the X power appears to be greater than the X to the fifth power at this point in time. Okay. And that viewing window goes from negative 6.6 to 6.6 on the X axis and from negative 4.1 to 4.1 on the Y axis. So now let&#x27;s change the numbers. Now I&#x27;m going to go with Zoom Standard number six, and that takes me from negative 10 to 10 on the X and y axes, and it appears as if we might be getting closer to an intersection point. Now I&#x27;m going to manually input some different window dimensions. And I don&#x27;t think we need all these negative values over here. So we&#x27;re gonna concentrate on going further in the positive direction and going further up in the positive Y direction. So what if we try negative too t eight to, let&#x27;s say, on the X axis. And what if we try? Um, negative 10 to 10,000 on the Y axis? Let&#x27;s go way up there and let&#x27;s make our scale go by one hundreds. The scale isn&#x27;t that important. It just is showing you how frequently you have a tick mark on your axis. All right, well, we see here that the the blue graph, which is y equals X to the fifth, is overcome by the red graph somewhere around here. So that tells us that the exponential function does grow more rapidly once we get to this point, whatever that is. So let&#x27;s go ahead and find that intersection point so we can go to the Calculate menu, which is second trace and then choose number five intersect put the cursor on the first curve. Press enter, but the cursor on the second curve. Press enter, and then you can move your cursor over closer to the intersection. Point and press enter, and we can see that that intersection point has X coordinate. Five. So that tells us that they intersect at the 0.5 comma 3125 and when X is large, the higher graph the red one. The exponential graph is growing more rapidly, So f of X equals five to the X, or its G of X equals five to the X grows more rapidly when X is large.

Carlos Pinilla · Answer

So here we have the functions. Eggs there lower well and the one that is always possible. That&#x27;s why to the next exposed so well, as you can see, those air Very different groups like these one x two feet. Sometimes they bury May, for you can see that foreign entity picks. He&#x27;s very with this one. So is increasing Always quality prison? Always. But But then sure is that both of these wolves are increasing. Right? Looks like our five. Thanks. Always Christian and so well, the only way you can see from the ground they only have a point of intersection right there. So world warm for seven. So they meet about around Thanks. Girls say it&#x27;s about 1.7 and as you can see here them they the exponential starts be your night. The exits are But then after that point, excessive give power his view Here young the explanation. So for thanks smaller than 1.5 from 1.7, you have try to be legs You&#x27;re done x to the fifth floor. Then from that point on extra, we&#x27;ll be here No, to be ex. Well, as you can see from that point on this looks this low is also beer grows faster. That condition is for thanks clearly so through at that point there, Ralph.

Problem

Make a rough sketch of the graph of each function…

Problem 44 Easy Difficulty

Compare the functions $f(x)=x^{0.1}$ and $g(x)=\ln x$ by graphing both $f$ and $g$ in several viewing rectangles. When does the graph of $f$ finally surpass the graph of $g ?$

Answer

$x \approx 3.43 \times 10^{15}$

Related Courses

Biocalculus Calculus for the Life Sciences

Related Topics

Discussion

Top Calculus 1 / AB Educators

Catherine R.

Kristen K.

Michael J.

Joseph L.

Calculus 1 / AB Courses

Precalculus Review - Intro

Functions on the Real Line - Overview

Recommended Videos

Watch More Solved Questions in Chapter 1

Video Transcript

James Stewart

Biocalculus Calculus for the Life Sciences

Catherine R.

Kristen K.

Michael J.

Joseph L.

Precalculus Review - Intro

Functions on the Real Line - Overview

What do you need help with?

Textbooks

Ask a question

Courses

AI Tutor

$x \approx 3.43 \times 10^{15}$

Biocalculus Calculus for the Life Sciences

Catherine R.

Kristen K.

Michael J.

Joseph L.

Precalculus Review - Intro

Functions on the Real Line - Overview

James StewartBiocalculus Calculus for the Life Sciences

Catherine R.

Kristen K.

Michael J.

Joseph L.

James Stewart

Biocalculus Calculus for the Life Sciences