Find limit at Infinity | sqrt(1+4x^6)/(2-x^3) x approaches infinity | general solution 

you're a genius, i tested by substituting the value of x to 10,000 integer and its came close to value of -2 , so basically any limits related to infinity, with any variables will only involve the power degree of the D and N from the expression, and other constants can be omitted, pure genius :) i love it

Theory says that if lim x --> a f(x) equals b, then lim x --> a (f(x))^2 equals b^2. So we can square f to get a simplified function of the form p(x)/q(x) where p, q are polynomials. This should trigger you, as polynomials simplify to constants when taking the derivative. So you can just start applying L'hôpital's rule however many times you need and doing this will give 4. Since this 4 represents the b^2, our answer is sqrt(4) = +/- 2. Sign analysis shows that in f, if x goes to infintiy we get inf/(-inf), so the -2 is the correct answer. Hence lim x --> infinity of f(x) = -2 Its an amazing way of getting rid of square roots. *Edit why the fk is my text crossed out

4 Because as we square up both parts Then we get (1+4x^6)/(4-4x3+ x^6) As x get to near infinity we had ((4x^6)+1 )/(1x^6) So 4 is nearly correct because 1/x^6 is too small

I was confused at first, but when you explained how to simplify with the 2x^2 + 5/3x^3 + 2x + 3 example, it made so much more sense

Don't you want to divide everything by the highest exponent from the denominator? So x^3? For the first example

Amazingly explained,thank you so much

You are a lifesaver

Thank you mam Rebecca.well xplained

I like it so much ❤

Good explanation 👍

Thanks!

Very helpful!!

Which country

👍👍👏👏

❤❤thank youuu

Thanks

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1/2

❤😮😂😅hi

Sono infiniti dello stesso ordine, immedito il limitr

you spent 8 minutes to do a problem that can be done in 8 seconds. you better not to upload videos any more

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