Question

lim x aprroachign 1 ( x-1)/(sqrt(x) - 1) = -2?

Answer 1

yo this is so hard omg

Answer 2

LOOOOOL!!!

Answer 3

lol

Answer 4

As soon as you start being nice, someone will be happy to help you

Answer 5

Well, if we substituted x for 0 we'd get 0/0, which is undeterminate. Therefore, you need to factor the function to see if there's any other way to get a solution.

So, since you have a square root, I'd try to rationalize the denominator. We'd get:
(x-1)/(sqrt(x) - 1) all of that times * (sqrt(x) + 1)/(sqrt(x) + 1).

After multiplying it out, we'd get:
(x-1)*(sqrt(x) + 1) all of that divided / (x - 1)

The x-1s cancel out and you get that the limit as x approaches 1 of that function is equal to the (sqrt(x) + 1). Substituting the x for the 1, you get 2. And that's the answer.

Answer 6

@Matt24 No giving away answers and don't do their work for them

Answer 7

Why? Sorry I'm new here. I thought that was the purpose(?)

Answer 8

No, we guide the asker.

Answer 9

@Luigi0210 is right. They are in Calculus now and they should be able to solve the problem with guidance. Only after they truly show efforts and still do not understand should you proceed to give them the answer so they truly understand.

Answer 10

Oh, damn. I thought doing it myself would help the person in trouble. At least I think I wouldn't mind getting an answer myself after asking, because usually going online is my last resort after having thought about the problem for a long time

Answer 11

Just to put my two cents in, we do encourage everyone to help the asker along instead of just providing them with the solution (regardless of how much work you show). Unfortunately, most people are not like you @Matt24 in that they think about the problem first. Many users just post questions in the hopes of getting a free answer. Those are the user you should report, and ignore.

Welcome to OpenStudy!

Answer 12

Oh well, thank you KingGeorge! I'm sorry for messing up :/

By the way, is there a section for Economics or Social Sciences here? Or is there only maths?

Answer 13

@Loser66 I've noticed buddy :3

Answer 14

http://openstudy.com/study#/groups/Economics%20-%20Financial%20Markets @Matt24

Answer 15

I agree with Loser66 that probably trying to explain is more time-consuming than just giving the answer. What happens if I spend lots of time online to explain sth to sbdy and then he or she doesn't really care?

Answer 16

@Matt24 Just click at the top where it says "Find More Subjects"

Answer 17

@abb0t @Luigi0210 Thank you! I'm going to check it out

Answer 18

So it's not wrong if I give an answer?

Answer 19

@Matt24 it is.. but chances are if you do you will get reported and get in trouble by the mods and such.

Answer 20

If you mean just giving them out directly

Answer 21

Oh lol it's a difficult system

Answer 22

It happens that you spend a lot of time carefully explaining something, and don't get anything out of it, you just learn to forget it and move on. Also, if you're halfway through your explanation, trying to get an asker involved, and they refuse to do so, don't be afraid to cut your losses and simply ignore the question until they start participating.

Answer 23

Oh ok. Thank you!

Answer 24

\[\lim_{x \rightarrow 1}\frac{ x-1 }{ \sqrt{x}-1 }\]
it can be solved two ways
1.
\[\lim_{x \rightarrow 1}\frac{ \left( \sqrt{x} \right)^{2} -1^{2}}{ \sqrt{x}-1 }\]
\[\lim_{x \rightarrow 1}\frac{ \left( \sqrt{x}+1 \right)\left( \sqrt{x}-1 \right) }{ \sqrt{x}-1 }\]
cancel the common and plug x=1 to get the solution.

Answer 25

2.

multiply the numerator and denominator by
\[\sqrt{x}+1\]
\[\lim_{x \rightarrow 1}\frac{ x-1 }{ \sqrt{x}-1 }*\frac{ \sqrt{x}+1}{ \sqrt{x} +1}\]
solve and get the answer