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Problem 60

Writing In Exercises 59 and $60,$ use a graphing utility to graph the function and estimate the limit (if it exists). What is the domain of the function? Can you detect a possible error in determining the domain of a function solely by analyzing the graph generated by a graphing utility? Write a short paragraph

about the importance of examining a function analytically as well as graphically.

$$\lim _{x \rightarrow 4} f(x)$$f(x)=\frac{x-3}{x^{2}-4 x+3}$$

$$\lim _{x \rightarrow 3} f(x)$$

Answer

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## Discussion

## Video Transcript

you're giving a function F of X is equal to actualize three over X squared minus four X plus three. You were asked to determine this graphically the London S X Airport history of effort. Lex The first well being graft this tar function and we can see that was it. But exactly three its entire functions on the fighting tutors holder. But around it it seems to be approaching on one side. 0.495 on your sides airplane 51 you can see that seems to be approaching 0.5. So we can say that the limit as export history of I flex is equal to 0.5. Next, we're asked to determine the remain of the function and we can see that there is also as in tow. Yet X is equal to one. And if we zoom outs, we can see it seems to go on continuously. So based off of this information, we know that the possible domain based off this graph this night Infinity 21 123 I know three to infinity. Now we're asked to determine why you can't determine the domain of the function solely by looking at what is generated by a graphing utility. Well, so you can't determine the domain of the function of the function. Your space. Okay. And you lied to analyze it because you won't be able to find to find any holes that are integral half can you or any as and hopes that are outside your window.

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