Could someone explain how the actual fuck the conjugate looks like in this example?...

Could someone explain how the actual fuck the conjugate looks like in this example?? I dont get it how the expression is solved

Lol, retard

/sci/
we're all retards here

ill gift a steam game if someone solves it with conjugates for me. I could easily do it by applying L'Hopital's Rule but that's not what i need now

L'Hôpital's rule

If you direct substitute the limit for the variable and end up with 0/0 or inf/inf, you can take the derivative of the top and the bottom at the same time to get a limit

Not all of us, but I'm lazy, and I'm sure the rest of the smarties are all out at this hour working real jobs.
Listen, I could do that, but I'm sure Wolfram Alpha has a handy tool to do exactly what you're asking for, why not use that?

Multiply the top and bottom by √y +1 (?)

Yeah ;^) but i really need to learn about conjugates

Wolfram alpha does it with L'Hopital's Rule

This is what i dont understand, where does the +1 come from? I tried solving it by multiplying with 4*sqrt(y)+3)

You can change the method you want it solved if there truly is more than one method. If not try another limit calculator web program

Fair, I see now that I've tried it myself. Have you checked their Forum? Sometimes you can find alternate ways to do problems by inputting specific terms.

are you asking how they got the given answer?

Do you know what a conjugate is?

x - 3 (conjugate is) x + 3

√y -1 (conjugate is) √y + 1

Yes

There's no √y -1 ....

what there to not get
factor the equation and remove terms that appear on top and bottom

You have to factor the top first, you silly goose

...

they are just factorizing the equation and cleaning it up.
it might make it easier for you if you substitute rt(y)=x and then try

The bottom factors as such:
y^2 - 1 becomes (y - 1) (y +1)

Then:
(y-1) becomes (√y -1)(√y +1)

Giving you:

(√y -1)(√y+1)(y+1)

Use your brain for once and do the work by hand, stop relying on programs with fixed algorithms that aim towards the simplest solution. Clearly whoever assigned this wasnt aiming towards the sinplest solution since that would be Hopital

Nobody has so far succeeded with factoring the top by hand. The bottom is the piss easy part

If you multiply (√y -1)(√y +3) you would see that it ends up as the original, so it does factor out

(√y -3)*

what are you talking about? it is already factored in op's picture

Im assuming that person doesnt see a quadratic term so they assume its unfactorable.

I am OP, im mainly wondering how the fuck someone figures that factoring out without using a calculator

OP: Are you just asking why the conjugate looks differently than what you'd think for this example?

They actually practiced factoring in highschool rather than relying on calculators to do their work for them

Substitute x^2 for y. Surely you know how to factor x^2-4x+3 and x^4-1...

...

LET w=sqrt(y).
do polynomial division or linear factorization, you mong.

inherent content knowledge?
Just convert it to a form you a familiar with (by subbing in rt(y) =x ) and then factorize then new equation and the convert it back

so you get:
x^2 -4x +3
=(x-1)(x-3)
sub back
=(rt(y) -1)(rt(y)-3)
easy

substitution is your friend

also this

>virgin handwriting

using your brain while doing math? Doing things by hand? Implying that isn't a fucking incomprehensible idea to most students nowadays. It's as pathetic as it is inexcusable, but it's a fact.

this tbh famalam
lemme break it down to ya
y - 4 * √y + 3
√y * √y - 4 * √y + 3
√y * √y - (√y + 3 * √y) + 3
(√y * √y - √y) - 3* √y + 3
√y * (√y - 1) - 3 * √y + 3
√y * (√y - 1) - 3 * (√y + 1)
(√y - 3) * (√y - 1)
literally EZ

brotip: remember
(x - a) * (x - b)
x^2 - (a + b) * x + (a * b)
substitute x = √y, a=1, b=3

op math is just made to confuse people

virgin indeed, as opposed to FUCKED.

fucking cancel out the sqrt y -1 because its in the numerator and denominator and then plug in 1 because the limit is approaching 1
God damn you're gonna fail calc 2 sooooo hard

these guys are doing something that should be very easy to understand

just forget about the sqrt(y) while you factor, sub for just x or y or whatever you choose, then put it back when you've factored the numerator

>people use calculators to factor nowadays
I work as a math tutor and if I ever saw one on my students using a calculator to factor I would tell them to stop. You should be able to factor in your head in middle school. Our educational system is sooo fucked.

Thank you guys for your help with factoring! I never before thought about that you can factor (x-1) to (√x+1)(√x-1) :/

>substitute rt(y)=x
What do you mean with this??

he means, to make factorization more intuitive just remove the sqrt(y) from the expression, and replace it with some other variable that symbolizes the same value; if you do this it should make the format of the quadratic more clear because ultimately the first term (y) will be equivalent to sqrt(y)*sqrt(y) which would be the newly substituted symbol squared

so

you'd get something like

x^2+x+1 where before x was sqrt(y)

So they factored the top and the bottom because when you plug in 1 you get 0 in the denominator.

The top is similar to factoring (y^2 - 4y +3), where you are looking for two numbers that have a product of 3 and a sum of -4. It turns out that -1 and -3 work, so you would factor the expression to (y-1)(y-3). You can verify that this works after FOILing. Your problem is the same but it has a leading term of y instead of y^2.

The bottom is a difference of squares that factors to (y+1)(y-1). Then, they factored (y-1) to (√y -1)(√y +1).

After factoring like so you simply plug in 1 for y.

This blew my mind that you can the 1 and 3 for the factoring by solving the 2nd degree polynomial