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University of California, Berkeley

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Problem 5

Estimating a Limit Numerically In Exercises

$5-10$ , complete the table and use the result to

estimate the limit. Use a graphing utility to graph

the function to confirm your result.

$$\lim _{x \rightarrow 4} \frac{x-4}{x^{2}-5 x+4}$$

Answer

$$\lim _{x \rightarrow 4} \frac{x-4}{x^{2}-3 x-4} \approx 0.20$$

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## Discussion

## Video Transcript

Okay, so we're asked to fill out this table song. Gonna plug in 3.9 into our function. We have 3.9 minus four, divided by 3.9 squared, minus five times people nine. But where when we get this is approximately no 0.34 Okay, let's start out with 3.993 point 999 The light it by 3.99 quid. When? A far from 3.99 What for? And we get 0.344 Okay, so now for 3.9 either and night. Punish boy. Delighted by 3.999 Good. Minus five times 3.999 What for? Only that 0.333 Okay, now it's a check for 4.2 ago. 14 point does that. One minus four. Divided by 4.1. Squared minus five times four. You know what that's more yet? 0.333 Get out with 1.1 Jack that before divide by 4.1 Squared, minus fired. Five times. 4.1. But what we get? 0.3 region and, uh, what, 4.14 point one when it's war. Bye bye. 4.1 thread my five times. 4.1 for what we get for you. 0.32 Great. Okay, so we could say that uh, X is equal to four. Our function or our limits approaching our function, is approaching 0.333