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Hi, can someone please help me with this:Find lim x→1+ f(x) and lim x→1− f(x),where f(x) = ( x + 3√ x − 1 if x ≤ 1) & (1 ...

Question

Hi, can someone please help me with this:Find lim x→1+ f(x) and lim x→1− f(x),where f(x) = ( x + 3√ x − 1 if x ≤ 1) & (1 − √ x − 1if x > 1)

Hi, can someone please help me with this: Find lim x→1+ f(x) and lim x→1− f(x), where f(x) = ( x + 3√ x − 1 if x ≤ 1) & (1 − √ x − 1 if x > 1)



Answers

Find $\lim _{x \rightarrow-\infty} f(x)$ and $\lim _{x \rightarrow \infty} f(x)$ for the given function $f$. $$ f(x)=\frac{2 x+1}{\sqrt{3 x^{2}+1}} $$

In even the well. I never skirted the banks minus squared on the X over X plus one Expletives air from the right and we can split into the two limit. Now one of us crammed. The next thing that you zero plus and minus limit under squaring the X off express one extract user plus for the first limit here is expected There are with a little PICO Judah infinity minus. For the second limit, we can push in Stein the square root They will have a square it on the limit off the x of a shanks plus one x two plus on here s extract User Plus, we're gonna from off the They're all the woman people choose their here If I get a good years old My nuts square root under zero over one And we're coaching infinitely. Man is on a coach Infinity

It was given. Don't leave it off the square root of the thanks. Minus one off the next minus one x, get you one in discussion here we don't need You used to love it and roll here. Indeed. We can run and he nominate the injured. A form skirt. The X minus one times skirted the experts born And that we say we can cancel the numerator with just one way have left. Good. Uh, let me have the one of us go to the express one Excellent. You won. And now, with they ever but the one inside and we get equal Judah 100 Jew.

Hello limit the attempts to one year to five limits get the terrorists to one. So the extension to one. This is extends to one screwed of X. My husband one it's minus developed by the play this the square root of X plus one. One is scheduled for this month. It is a 004 So will multiply with this. So it will be closed to limit X dash one X minus one. That's my husband. Special effects. Yes but so we cannot get limit extends to one one of our schools. There's one that is not the customer and he had access approaches to one. So now we will for the value to what that cost 2.5. They both leadership. Thank you.

So for this given problem, we want to evaluate the limit. Um and this is going to be a problem 59. So it's gonna be the limit as X approaches one of the square root of x minus one, and then this whole thing is going to be divided by x minus one. Um And we're finding the limit as X approaches one. So the way that we can do this is by multiplying the top and bottom by route X plus one plus one, that's what's known as the conjugate. So we could end up doing this. But we see that the limit as X approaches one from the right is going to end up being all right, is going to be this value right here, but we have nothing as it approaches from the left. So we're seeing that as we approach here it's undefined. But approaching from the right, we get very close to one half and approaching from the left were very close to one half. So based on that we say that the limit is exactly one half


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