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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_{p \to -1}\frac{1+p^9}{1+p^{15}} $

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Calculus 1 / AB

Chapter 2

Limits and Derivatives

Section 2

The Limit of a Function

Limits

Derivatives

Gino C.

October 9, 2020

Campbell University

University of Nottingham

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.

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his problem. Number twenty Poor Stuart Calculus, eighth edition section two point two Use the table of values to estimate the value of the limit. If you have a graphing device, easy to confirm your result. Graphically. No limit as p goes to negative one of one plus Peter the name divided by the quantity one plus p to the fifteenth. Now, in order to eat, estimate this limit. We would like to choose values and create a table to evaluate this function at values around negative one. As you can see in this table, we have chosen values to the left of negative one so slightly less negative. One point Oh five negative one point one ada one point o one and so on. And the closest value that we choose that is closest to negative one is negative. Zero point five nine nine nine eight two If we approach it, need one from the right values that air slightly greater than negative one. We see that we begin here a negative point nine five, and as we get closer to negative one, we reach this point, which is evaluated at P equals negative point nine and nine nine nine nine and we reach a value of point six zero zero zero or one. And what this is supposed to show us is very close estimate as to what number dysfunction is approaching as P goes to negative one. Since the function is in undefined at P equals two negative one and we heat. We see here that AARP assessment would be to say that the function approaches the value of zero point six. Now we're going to use a graphing device. We're going to use it plot in this spreadsheet to confirm our result. You are also able to use a graphing calculator or any other graphing tool ontake dysfunction and plotted around the very around this specific value that we're looking at negative one and then we do a plot. Around here, we see that the behavior of the function as it approaches. I think the one from the left is that it approaches value zero point six. The function of the from the behavior of the function as we approach negative one from the right is also approaching zero point six. And this graphing tool has been able to help us confirm our estimation that this limit is equal to their point six

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