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University of California, Berkeley

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Problem 13

Estimating a Limit Numerically In Exereises $11-18$ ,create a table of values for the function and use the result to estimate the limit. Use a graphing utility to graph the function to confirm your result.

$$\lim _{x \rightarrow 1} \frac{x^{4}-1}{x^{6}-1}$$

Answer

$$\lim _{x \rightarrow 1}\left[\frac{x^{4}-1}{x^{6}-1}\right] \approx 0.67$$

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## Discussion

## Video Transcript

Okay, so we're asked to create a table. So let's start with the value from left high. So something to the left of one. That's 6.9. So that's gonna be plugged into our own shindo 0.94 minus one over 0.9 feet about six minus one, which is approximately 0.73395 So we're gonna do the same for exiting 2.99 and then our function. Our function approaches 0.67 DRI dri. Now, if I actually could 0.999 our function approaches 0.667 drinks three valleys from what? The right hand start inside. Let's start with Axity conceded one point. Does one in our function approaches 0.666? That was quick to 0.1 point 01 Our function is approximately 0.66 and when actually could do 1.1. Our function is approximately 0.6015 as we approach one from the left hand side and the right hand side for approximately approaching 0.67 So the limit and experts one of our function is approximately 10.67