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Problem 28 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_{x \to 0^+}x^2 \ln x $

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Video Transcript

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.