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2/7 points Previous Answers LarCalc11 2008_My NotesAsk Your TeacheComplete the table. (Round your answers to four decimal places:) lim Ix + 1) _ (44) X-3 X - 32.92....

Question

2/7 points Previous Answers LarCalc11 2008_My NotesAsk Your TeacheComplete the table. (Round your answers to four decimal places:) lim Ix + 1) _ (44) X-3 X - 32.92.992.9993.0013.013.1f(x)XX3Use the result to estimate the limit. Use a graphing utility to graph the function to confirm your result: (Round your answer to four decimal places: = lim I!x+1= (44) ~ X73

2/7 points Previous Answers LarCalc11 2008_ My Notes Ask Your Teache Complete the table. (Round your answers to four decimal places:) lim Ix + 1) _ (44) X-3 X - 3 2.9 2.99 2.999 3.001 3.01 3.1 f(x) X X 3 Use the result to estimate the limit. Use a graphing utility to graph the function to confirm your result: (Round your answer to four decimal places: = lim I!x+1= (44) ~ X73



Answers

Complete the table and use the result to estimate the limit. Use a graphing utility to graph the function to confirm your result. $$ \lim _{x \rightarrow 3} \frac{[1 /(x+1)]-(1 / 4)}{x-3} $$ $$ \begin{array}{|l|l|l|l|l|l|l|} \hline \boldsymbol{x} & 2.9 & 2.99 & 2.999 & 3.001 & 3.01 & 3.1 \\ \hline \boldsymbol{f}(\boldsymbol{x}) & & & & & & \\ \hline \end{array} $$

Okay. So if you look at this situation that's fine. That's completely the table. Okay? By filling out all the Corresponding y values when x equals -3.1. Why? It goes -0.2 48 Fine. Okay X equals -3.01. Why you Cause By the 0.248? But exit cause by the 0.3001 Why? You cost 3.249 2450. Okay Well actually it goes to -2.989. Why are you cause minus their little point? Sorry I made a mistake here. So this should be uh -0.25. Okay. And the next is also by this little .25. Blacks equals -2.99. This is the 4th -2 points five but they still want to Fine. Okay. And 2502 And Ux x equals -2.9. Yes you close -0.2516. Okay so you can see yeah -3 is between these two numbers. So the limits, It's also between these two values which is -3.25. So this limit equals -0.25. Okay and uh you can check this on this graph. Okay. S x approaching minus three, you can see the value, It's approaching -3.25. Okay. The y value that for the functions value It's a approaching -3.25

So today we have the following limit and we want to A to get done approximate value by a getting approximate values near x three. So in order to do this, we need to construct a table off the values for X on the function. So what We half is here x on Dhere. We're going to put the values off the function, okay, and let's see how it behaves near three. So let's start with 2.9. Then let's go with 299 Then we're going to get the values off to 999 and then we go for values that are bigger than three like 3001 Then 301 on finally value, that is 31 So let's see how these values off X on. This is just minus zero 06 four. Then we got values off 0.0 six 26 than here. Where is the value that is really near to three? We get a value of 0.6 25 than for values that are greater than three. We get the following values 2.6 24 Here we got a value of 0.6 23 Andi, Finally, we got a value of 0.6 06 nine. So, as you can see, we're approaching to the value that is near toe minus 0.0 uh, 625 either from below X or from above X. So from here, we can get an approximate value for this limit, which is going to be minus 0.0 6 to 5. But, uh, let's just making a little bit off algebra. You can check that this is approximately one divided 16. So this is the real answer. Or you can just put, uh, or just can put minus 0.6 to 5. There is no problem. Then we can check this graphically on Dhere is our plot. This the function that we have on Duh. So the values that approach to three are, as we can see, your 30.6 Well, we got a little bit more position we're going to check. That point is going to evaluate us a minus one over 16 and that's all

Okay, so it's time. We want to find the limit as X approaches. Three. So, looking at three, if we're approaching it from our left at our right, we're approaching the same valley. So this value is approximately. Is there a point for six? So we see there are limit value is approximately 0.46

Okay. So this time we want to find a limit as X approaches one. So let's approach that from our left and a right. And we're approaching that same value. So this is a between their on one, and this is actually it looks like approximately vera 0.8.


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