Download the App!
Get 24/7 study help with the Numerade app for iOS and Android! Enter your email for an invite.
Question
Answered step-by-step
Use a table of values to estimate the value of the limit. If you have a graphing device, use it to confirm your result graphically.
$ \displaystyle \lim_{x \to 0^+}x^x $
Video Answer
Solved by verified expert
This problem has been solved!
Try Numerade free for 7 days
Like
Report
Official textbook answer
Video by Leon Druch
Numerade Educator
This textbook answer is only visible when subscribed! Please subscribe to view the answer
02:47
Daniel Jaimes
Calculus 1 / AB
Chapter 2
Limits and Derivatives
Section 2
The Limit of a Function
Limits
Derivatives
Missouri State University
Campbell University
Harvey Mudd College
Boston College
Lectures
04:40
In mathematics, the limit of a function is the value that the function gets very close to as the input approaches some value. Thus, it is referred to as the function value or output value.
In mathematics, a derivative is a measure of how a function changes as its input changes. Loosely speaking, a derivative can be thought of as how much one quantity is changing in response to changes in some other quantity; for example, the derivative of the position of a moving object with respect to time is the object's velocity. The concept of a derivative developed as a way to measure the steepness of a curve; the concept was ultimately generalized and now "derivative" is often used to refer to the relationship between two variables, independent and dependent, and to various related notions, such as the differential.
0:00
Use a table of values to e…
02:14
02:17
03:06
04:07
01:06
All right. We want to make a table of values to try to uh see if the limit of X to the X power as X approaches zero from the positive side uh exists and what it might be. So we're going to have a few X values that are approaching zero from the positive side. It's a 00.1 than a little closer to 0.1 than even closer 0.1. And then really close to 0.1. And so we want to calculate what is X to the ex uh the nexus 0.1, we're going to have 0.1 Raised to the .1 power. When next is .01, we're going to take .01 Raised that to the .01 power. Let me rewrite that. And some of these might get so small for the calculator that I might not even actually be able to calculate them. But for X equal 2.1 X dx 0.1 to the 0.1. So let me pause this video and see if I can get some of these numbers. Okay, so kind of surprising. Um I thought these would be really tiny numbers, but when I did 0.1 race to the 0.1 power, I got approximately 0.79 point oh one race at a point a one hour I got 10.95. So I thought they'd be such tiny numbers that calculator wouldn't even show it. Um but they're actually, you know, .95. The next 1.001 raised to the 0.1 hours 0.993. So we can do one more. Uh Let's do When X. is zero. The nexus .0001 X. To the X. is .0001 raised to the .0001 power. And if I put that in the calculator let's see what I get .0001 raised 2.0001. And I get .999. So it looks like as X is approaching zero from the positive side. It looks like the function values. Uh They look like they're approaching the value of one. So let's take a look at the graph of the function X. To the X. Power. And let's look what happens to that graph as we approach zero from the positive side. So here's a graph of X. T. X. And I put restriction on the X. Values X has to be greater than zero because X is approaching zero from the positive side. So it never actually become zero. It just gets close to zero from the positive side. And I kept X greater than zero when I graft to function X. D. X. Because it's not defined when X is zero. You would have 0 to 0 which is undefined. Um You can actually see that if you try to get this point right here, Okay affects 02 functions not even defined, but you can see that as X approaches zero from the positive side. Uh Let's look at the function values 00.7 point 74 Point 80.8 4 .9 .9 1 .929397. I see you can see um that as X approaches zero from the positive side, the function is approaching the value of one.
View More Answers From This Book
Find Another Textbook
03:01
A magazine provided results from a poll of500adults who were asked t…
02:40
If you draw a card with a value of five or less from a standarddeck of c…
01:55
Construct a 90% confidence interval for the population mean, μ.Assume th…
03:28
Demand for oil changes at Garcia's Garage has been as follows:Janua…
05:59
Myron Corporation is sponsoring a walking race at its companyouting. Leo…
03:27
A manufacturer knows that, on average, 2.4% of the electrictoasters that…
06:47
An engineer working for a manufacturer of electroniccomponents takes a …
04:15
In a certain survey,516people chose to respond to this question: &qu…
02:08
Containers of oats are prepared in advance for a baking project.Later, r…
01:53
Assume that the sales of a certain appliance dealer areapproximated by a…