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(a) Use a graph of $$f(x)=\left(1-\frac{2}{x}\right)^{x}$$to estimate the value of $$ \lim _{x \rightarrow \infty} f(x)$$correct to two decimal places.$$$$(b) Use a table of values of $f(x)$ to estimate the limit to four decimal places.

(a) 0.14(b) 0.1353

Calculus 1 / AB

Chapter 2

Limits

Section 2

Limits of Functions at Infinity

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So for this problem, we're supposed to graff the dysfunction and, uh, with the help of technology and create a table without of technology of its values to estimate it to the 1st 2 correct distant places with the graph and for desolate places with, uh, a table of values. So I used ah, very helpful website Dismas desmond's dot com, Dismas and ah, I mean, you could probably use well from Alfa or, um, a graphing function like graph for on your on your Macintosh or ah, good old fashioned calculator like T 84 above. And, um, basically, you're allowed to, uh, plug in the function year of of X equal to one minus two over X to the X and plug in any number of values. And I just picked fund values pretty large values, um, and, ah, to get an idea of where the where the function would converge as X goes to infinity. And so you see, at 20,000 you get ah, 0.1353 Um, if you round 24 decimal places in that 2000 you get 0.14 If you round to two decimal places, um so but to make our lives easier, we don't have to zoom in that much because we can use a function of decimals where if you put the cursor over the function, it tells you the value at that point. So at exits 2000 we get to approximately 0.14 So we can just say that we drafted an estimated, um, the function to convert something like 0.14 Um, because X is rather large 2000. And for ah, our estimates, four different places. We just used the table here and plugged in 20,000 and got something around your 40.1353

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