Limits at infinity of quotients with square roots (even power) | AP Calculus AB | Khan Academy

Limit at infinity of rational expression with radical.

AP Calculus AB on Khan Academy: Bill Scott uses Khan Academy to teach AP Calculus at Phillips Academy in Andover, Massachusetts, and heÕs part of the teaching team that helped develop Khan AcademyÕs AP lessons. Phillips Academy was one of the first schools to teach AP nearly 60 years ago.

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[milestonekennedy]

you have to find the square root of calculus with nothing but an order of operations sequence to find negative square roots, which are necessary to find the how much our gravity will reverse from electricity.

[emoryfelice]

For those saying that the answer should be -1, let me just clarify why it's not (it took me a minute when I was trying out the problem before seeing the rest of the video).
If you were to instead do the problem by disregarding the -x in the numerator and the 3 in the denominator (which is similar to the method Khan used in the video with odd powers), to leave you with √(4x^4)/2x^2, you might see that better. By taking the principle root of (4x^4), you get |2x^2|/2x^2.

Remember that the exponent is EVEN, which means that plugging in any negative number for x will just yield a positive one after it is squared. Since that means that both the numerator and denominator would be positive (the numerator because it is in absolute value brackets and the denominator because the exponent is EVEN) even for a negative number, the answer for the negative infinity is still positive 1.

By the way, graphing the function or making a table would, indeed, confirm that for anyone still confused.

[brklynkiwi]

That was so helpful thank you so much!

[nilukiperera]

THANK YOU SO MUCH. I FINALLY UNDERSTAND

[abcd]

Please do video on "Orthogonal Trajectories by Differential equation". Please please please

[husamzrikat]

The answer must be - 1, in - infinite multiply by -

[brendonchirume]

i used a different method i removed the radical sign by raising everything to the power half... is my method accurate !!

[arfasarfraz]

but if we have function |n/(n-2)^1/2| with n tends to infinity then what will be its limit?

[Aria-louk]

Couldn't you just take square root of 4x^4 and simplify that to 2x^2 then divide that by the 2x^2 on the bottom to get the 1

[wancarrie]

Can someone explain how sqroot(4x^4-x/x^4) is equal to sqroot(4-1/x^3)?

[Ulas_Aldag]

And by what I have to divide if both don't have the same grade?

[chadcite]

should the answer me -1 ? instead of positive 1 ?

[emonyankitteh]

Couldn't every term in the function also have just been raised to the ^2 power. I don't understand why this wasn't also looked at as a valid way to prove the lim = 1. If you square the numerator and denominator you end up with two terms of = highest degree which usually means the limit will be a quotient of those two terms. This also would have given 1 and seems like a much less convoluted way of solving the problem. Am I missing something here or was this just used as a way of PROVING the highest degree numerator = highest degree denominator trick of solving these.

[yahairareyes]

can someone explain how 1/x^2 is multipled with sqroot4x^2-x

[miadoniz]

i think it should be negative because the x approaches to negative infinity

[abdullahiomar]

The answer should be -1 because we are approaching negative infinity.

[pramodsharma]

If you are multi placating 1/x, it means you are multi placating it with 0. So please reply it

[majidalbarram]

I swear this is useless like on your app it doesn't stay constant on why it's negative or positive while solving it doesn't make sense whatsoever