Problem 24 Easy Difficulty

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}} $

Answer

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Video Transcript

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