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Use a table of values to estimate the value of thelimit. If you have a graphing device, use it to confirm yourresult graphically.$\lim _{x \rightarrow 1} \frac{x^{6}-1}{x^{10}-1}$

$$\lim _{x \rightarrow 1} \frac{x^{6}-1}{x^{10}-1}=0.6$$

Calculus 1 / AB

Chapter 1

FUNCTIONS AND LIMITS

Section 3

The Limit of a Function

Functions

Limits

Continuous Functions

Campbell University

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University of Michigan - Ann Arbor

Lectures

03:09

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So we're going to estimate the value of this limit by making a table. And what you're going to want to do is the pick values that are around wine. So what I'm gonna dio is I'm gonna use the values 1.1 one point syrah wine and 1.1 And I'm going to take some points from the other side. A 0.9 point 99 and 990.999 You wanna set them up? So the points get closer to the number in this case wine. It's that way. It will be easiest to figure out what the women is. So we just take these values and pulling them in for X. And what you get is point for a four 0.588 0.599 0.719 point 612 and 6120.601 So if the first set of points it looks like it's getting closer to six and off the second to the points, it's getting closer to six. Her 0.6, I should say so that means they're limit is 0.6. And again, you could have gone about this slightly differently and got in the same and syrah

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