Evaluate Limx->1? I cant figure this out

[Stevo11]

Homework Statement

Evaluate this Limit

lim┬(x→1)⁡= (√x-x²)/(1-√x)

The Attempt at a Solution

So What I did at first was obiviously sub'd in one and got "0"/0, undefined. So then I started to try and simplify the function by multiplying it by its conjugate, but I got some
"unfactorable mess" So then I proceeded to try and use Quotient/product rule to derive it then sub one in, I still keep getting a mess of Fractional exponants and winding up with zero...the only way I can solve this is with L'hopitals Rule.. but surprise surprise... we're not allowed to use this rule!

Yeah sort of at the end of my rope with this question and my proff's are useless as usual, they just keep telling me to try harder, but Damn it I'm awful at math, I'm going to school for Ecology but need Calc and physics, so I'm trying here but getting absolutly no where...

 

[1mmorta1]

I'm on the run, so I haven't looked at the problem closely. Try dividing top by bottom and then subbing in x =1

 

[verty]

You need to simplify the right hand side. It can be done. A hint: use the substitution $a = \sqrt{x}$ to make it easier.

 

[Stevo11]

ok so I simplified the top and now I'm stuck with

x(1-x)/(1-√x)


it still comes to zero... I think the answers supposed to be 3.. ugh fml with calculus

 

[SammyS]

So, the problem is to find $\displaystyle \lim_{x\to1} \frac{\sqrt{x}-x^2}{1-\sqrt{x}}\,,$ I take it.

theFactor √(x) out of the numerator. You then have √(x) times the difference of cubes: 1-(√x)³. Factor the difference of cubes.
$\displaystyle \lim_{x\to1} \frac{\sqrt{x}(1-(\sqrt{x})^3)}{1-\sqrt{x}}$

 

[1mmorta1]

what did you get when you factored the top and the bottom?

 

[Stevo11]

Thats the thing! I don't know how to factor a difference of cubes, I got thrown into calculus and I don't know math, and my teachers won't help me, do I cancel out all the Root X's?

 

[1mmorta1]

You want to get rid of the bottom, so you have a continuous function. Do you see how you might do that? From what sammys did?

 

[Stevo11]

so when I take a differece of cubes of the top I get


√x(1-√x)(1²+√x+√x² Over 1-√x

then the 1-$\sqrt{x}$ cancel and then when I sub one in for all the X's I end up with 3/1 which is the right answer.. um yeah I'm confused

 

[vela]

That's the thing! I don't know how to factor a difference of cubes. I got thrown into calculus, and I don't know math. and my teachers won't help me. do I cancel out all the Root X's?

I wouldn't be too worried. I'll bet others in your class feel the same way about having forgotten a lot of math. You'll have to relearn some algebra, and this time it'll tend to stick.

You just need to understand you're at the point in your education where you're expected, on your own, to refresh your memory on stuff you learned before and may have forgotten. That's likely why your teacher isn't so forthcoming with helping you with basic algebra.

so when I take a difference of cubes of the top I get √x(1-√x)(1²+√x+√x² Over 1-√x

then the 1-$\sqrt{x}$ cancel and then when I sub one in for all the X's I end up with 3/1 which is the right answer.. um yeah I'm confused

Yup, that's it.

 

[Stevo11]

Oh man I don't know how to thank you guys enough lol, really thanks a million for all the help, I officially love this forum :) :) :)

and yes I know I should know some math, but yeah, its sort of my achillies heel with Univ. I know my Bio/Chem like a pro, hell even physics I'm good at because I can set up problems wrap my head around concepts, but Calc/Functions is just like.. what is happening here?

 

[1mmorta1]

Don't worry, limits is really the only part where you will struggle with the algebra. It sounds like your at the beginning of your calc course, from here on out, most of the material will be new concepts.