Calculus Limits at Infinity with Square Roots

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Calculus Limits at Infinity with Square Roots.
The question is to find the limit as x approaches negative infnity of -5x/sqrt(2x^2 + 11).

[@Petrichor_Pyroclast]

"The Math Sorcerer" is a good name, but "The Mathmagician" would be better.

[@TheMathSorcerer]

[@teefas4476]

Thank you 🙏🏼

[@meroyohan9121]

Legend

[@TheMathSorcerer]

:)

[@omgdeann4ever]

it wud be -5 not 5 !!

[@carloserr1435]

I understand what's going on but need help with one step. At 2:28 you begin to evaluate the limit and it's the denominator which confuses me. How are you evaluating it? It looks like you're using theorems to evaluate it but I can't think of any which apply. I understand, for example, that lim [f(x)]^n as x approaches c is equal to [lim f(x) as x approaches c]^n but that only applies whenever you let n be a positive integer (according to my textbook). lim 5/root(2+11/x^2) as x approaches -inf should be equal to ratio of the value of the limits of the top and bottom, no? If possible could you clear up that step for me? Thank you.

[@brandonheath6246]

Can you write the final as limit equals 5 ➗️ the square root of 2

[@ivanjin9989]

limx-negative infinity ( 7-3x^3)/(2x^3+1) we need to divide everything by x^3 so get the answer is -3/2 but we divided by x^3 and x is negative ,why we don't need to change the sign here ? so confused !!!!!!

[@angelmendez-rivera351]

You divide both the numerator and denominator by x^3, so the sign is irrelevant. You are multiplying by 1.

[@shahriarmim4696]

how sqrt x^2 = -x ? The numerator will be -5 not 5 ! :)

[@angelmendez-rivera351]

sqrt[(-5)^2] = 5 = -(-5).

[@nicogehren6566]

nice

[@intros1854]

Thanks

[@1TopGunPaintballer]

This does help. You use the same pie wise function as my professor with sqrt(x^2) I've searched all over the Internet and my textbook to find an example like: (Lim X-> -infinity) x*sqrt(x^2 + 2x) I can not find a similar problem with just a radical. If it was like X+sqrt(x^2 + 2x) I would multiply the numerator and denominator by its conjugate. But with just a radical I am stumped. Can someone explain or direct me to a video?

[@noorazieramusa1426]

why √(x^2)=-x ?

[@TheMathSorcerer]

+Noor Aziera Musa x -> -inf, so x < 0, so sqrt(x^2) = |x| = -x

[@noorazieramusa1426]

+The Math Sorcerer thanks mister,good video and have a good day😊

[@omgdeann4ever]

this is completely wrong

[@angelmendez-rivera351]

No, it is correct. See my comment.

[@bassboosted4025]

lifesaver. kudos to google as well for pointing me to the right video