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3x-2 Letf(x) be a function that satisfy the following inequality < f(x)3xl+7 for all x > 20. X(a) State the Squeeze Theorem(b) Apply the Squeeze Theorem to fi...

Question

3x-2 Letf(x) be a function that satisfy the following inequality < f(x)3xl+7 for all x > 20. X(a) State the Squeeze Theorem(b) Apply the Squeeze Theorem to find the limit lim f(x). Justify your answer: X+0

3x-2 Letf(x) be a function that satisfy the following inequality < f(x) 3xl+7 for all x > 20. X (a) State the Squeeze Theorem (b) Apply the Squeeze Theorem to find the limit lim f(x). Justify your answer: X+0



Answers

Find the limit of each function (a) as $x \rightarrow \infty$ and (b) as $x \rightarrow-\infty .$ (You may wish to visualize your answer with a graphing calculator or computer.) $$f(x)=\frac{2}{x}-3$$

We have to follow in function if that is a piecewise function. And given the avenue to first in the limit as X. Goes to two from the left side, a couple of eggs. And since it's from the left, I need to look at the case of less than two, which is going to be X squared plus six Or to scare plastics issues at 10. Then we have a limit at the X Custer too from the positive of effect This part where is pas Arabia to look at this one. X. Great and equal to two, which is going to give us too cute close to two. And given them to find the limit attacks goes to two of F of X. That's that's the limit is the same from left and the right. Then the overall limit is also going to be 10.

We are given the following piecewise function and having this, we need to determine time limits. So our function is uh x squared plastics for excellence in two And x cubed plus you for extraordinary equal to two. The first thing we need to find is the limit as X goes to two from the left side of F a bex. But since you're going to to from the left side, that means X is going to be less than two, which means you need to use export plus six for our functions. This becomes the limit as X. That's the two of X squared Plus six. Looking in the two, that's going to give us a four and you get 10 as our final answer next, we're finding the limit has eggs Goes to two from the right side of F of X. Now if X is going to to from right side That means X is going to be greater than two. So we're gonna use execute plus two here, that's becomes the limit as X. First the two on the right side of X. Q Plus two and ethics goes to two, x cubed goes to eight and the entire limit becomes set. Now, finally, we need to find the limit As X goes to two of eggs. Generally. Now the limit, ethics goes to any value generally is going to be the same as it goes to the left side and the right side. So if they're so values from the left and the right sides are different, Then there is no limit but here they are the same. They're both 10. Therefore, the general limit also becomes sent and our answers are 10 and 10 and 10, and so we're done.

So we had this peaceful eyes a function definition for F. Given that we need to find the limit and X goes to two from left um from left of F. Of X. And that if that's the case, we need to look at the case when X is less than two. Are we going to have two squared plus five or nine? Next part? We need to find the limit. I'd like to close to two from positive from the right side. Other Quebec's. We need to look at this scenario excreted and according to That's going to give us too cute. Close one or 9 again. Now having those two, we need to find a limit. Medics goes through to generally open phobics Since 11 is nine from both left and the right. That the overall answer is also night really?

So we have the following piecewise function for F. Mx and that is X. F of X. Is X squared plus five. Given X is less than two. An X cubed plus one. Given X is greater and record to to so having the following functions you need to calculate the limit At the X goes to two from the left side of F of X. It's exposed to too from left many X is going to be lesson to which means instead of F of X, I can just write the limit as eggs goes through to of X squared class five and as exposed to two, X square plus five will go through four plus five or nine. Next we need to calculate the limit. Adex goes to two on the positive side of F of X. F X is going to do from the right side. Many, many actually had this function and we have X cubed plus one. It's also going to get the limit I was exposed to too. Opec's cube plus one, Annex Cuba will go to eight. So the whole thing will go to eight plus one or nine. Now we need to find a limit at the exclusive to. Now therefore bags. Now this is gonna be the same as both the limit from the left on the right side and so because they are the same and they're both nine. Therefore we have a limit of nine for generally as X as explosive too. And so we're done


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