another problem

[unique nebula]

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[shut ermine]

i also have a handful more of problems that i need help with too, so if anyone is able to help me with those that would be great too!!

[olive lark]

are you allowed limits

like is this calc class

[shut ermine]

yep

[olive lark]

oh ok

try facotring x out of the initial sqrt, does that do anything interesting?

just think about lim x-->inf

[shut ermine]

wait how would i do that

like wdym

sorry

[olive lark]

have you seen the polynomial division limits before like (let me type an example)

$\lim_{x\to\infty}\frac{x^4-3x^3+4x-3}{5x^4+5x^3+5x^2-23}$

[stuck lava]

doggo with da hat

[olive lark]

do you know how to solve those

[shut ermine]

yes, that would be 1/5 right?

[olive lark]

yea

do something similar with the other one

how do you solve those btw is it through lhopital or facotring out x^4

[dull star]

both work

this one is a bit different though
$\sqrt{9x+1} - \sqrt{9x}$

[stuck lava]

cute rizzly bear (nom nom nom)

[dull star]

subtraction, not division

[olive lark]

||grrr trying to explain why we can just ignore the +1||

[dull star]

in this case it is because the derivative of square root goes to 0

idk if the OP is in calculus

lemme see if theres a better way

oh yeah there is but idk how to guide you to it

[olive lark]

yes

[shut ermine]

I just looked at the degrees of the polynomial on the top and bottom

so idk if i can do that with this one and I don't know any other way to do it

[shut ermine]

I am, this test is on differentiation apparently

this is a practice test btw not the actual test

[forest mortar]

I reckon it is hard to see the tendency of a difference of two radicals, both tending towards positive infinity as x tends towards positive infinity

How about we "de-rationalize" it, making it a quotient of radicals, where the denominator is a SUM of the monomials instead of a DIFFERENCE?

Then we know for sure that the sum in the denominator tends towards positive infinity