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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^2 \ln x $

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Calculus 1 / AB

Chapter 2

Limits and Derivatives

Section 2

The Limit of a Function

Limits

Derivatives

Oregon State University

Harvey Mudd College

University of Michigan - Ann Arbor

Idaho State University

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.

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This is problem A number twenty eight Stuart Calculus, eighth Edition, section two point two. Use table values to estimate the value of the limit. If you have a graphing device, easy to confirm your result graphically. The limit as X approaches zero from the right of the function X squared Tamil Allen of X for this problem, since it's a limit as experts zero from the right or from the positive side, we will only be choosing values that are positive. Ah, and very small, very closer to zero. As you can see in our table, we have chosen values such a zero point five zero point one and getting increasingly smaller but still larger than zero. And if we look at the calculations done using the function given using each of these X's valleys, we see that the value is that negative number in this range and gets increasingly smaller, increasingly closer to zero. Here, we're very, very close to zero. And what we can estimate at this point is that the limit as X approaches zero from the right is that this function will approach it. Zero. We're going to confirm our result graphically using a plot in the spreadsheet. You can also use a graphing calculator or another graphing tool and plus X squared times E clinics around X equals zero, but not to the left on ly to the right as we're looking for the limit as experts, zero from the right and as we see from the right, the function this whole stream closer to zero as Ex gets closer and closer to zero, and with his confirmation, we can conclude that dis limit is equal to zero.

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