use calculus to approximate 1.999^4 (no calculators)

[@DrBarker]

I actually got the same answer by finding the first 2 terms in the binomial expansion of (2+x)^4, with x = -0.001. Neat!

[@user-wu8yq1rb9t]

The Beautiful Mind, Dear Dr Barker is here ... Cool. Binomial? You made a video about it? I should check your channel, yes.

[@kobethebeefinmathworld953]

I think this should always hold because the linearization method in calculus is using Taylor expansion and ignoring all terms after 2nd derivative, where the term with the 1st derivative is exactly the same expression as the 2nd term in the binomial expansion of the shifted function.

[@teelo12000]

How to approximate 1.999^4 whilst using a calculator: 1. type in 1.999^4 2. add 0.0000000001 to the answer, because we want an approximation, not the actual answer

[@GodbornNoven]

lol

[@geraltofrivia9424]

Easier to use the formula directly with x = 1.999 and a= 2, that gives L(1.999) = 16 + 32*(-0.0001) = 16 - 0.032 = 15.968. Trying to simplify the general expression of L(x) leads to a more complicated calculation in this specific case.

[@ChristAliveForevermore]

BPRP: use calculus to approximate 1.999^4 (no calculators) Also BPRP: *uses calculator*

[@jamescollier3]

forest trees

[@ΑΝΤΩΝΗΣΠΑΠΑΔΟΠΟΥΛΟΣ-ρ4τ]

another way of calculating 32*1.999 at the last step of the linearization, could be writing 1.999=2-(1/1000) and then proceed with applying distributive property: 32*1.999-48 = 32* (2-1/1000) - 48 = 64 - 0.032- 48 = 16 - 0.032 = 15.968

[@fadoexplains2837]

Yup

[@flowers42195]

Yes good, the same as i thought that make it so easy without calculator

[@yaskynemma9220]

The first was easier to compute before distributing the 32, I even think that the 2 methods look the same in that step, but as always maybe there is a detail that dont make them the same and that I am missing because I am not a mathematician

[@gerryiles3925]

You should have left off at L(x) = 16 + 32 (x - 2), or better, since wanting to use a number less than 2, L(x) = 16 - 32 (2 - x), then it is basically the same as the differential method...

[@bprpcalculusbasics]

Ah yes. That would have been much better

[@NoNameAtAll2]

dear Just Calculus, can you please add main channel (RedPenBlackPen) into "Channels" submenu of this channel? This would allow for better navigation on mobile than "main channel" button in "About" submenu

[@helgen3821]

Best approximation of (1.999)^4 is 2^4 I think

[@nick46285]

not accurate enough without calculus

[@evanlawrence]

@@nick46285 As an engineer, this is good enough for me

[@sleepingboiz8155]

For me I just did 2 to the power of 4 then minus 0.032

[@beabzk]

Him: no calculators Also him: uses calculator for 32(1.999)

[@VincentCSPG3D]

I watched this before on your main channel and I liked it very much lol

[@carlossecas2756]

great explanation

[@lekanakinwale8411]

Using binomial theorem to approximate>>>

[@user-wu8yq1rb9t]

*Calculus not calculator* ... *I love it* Thank you Teacher 💖

[@fernandofa2001]

Very interesting!

[@Anti_Electron]

I tried this method using a random number like (2.3)^4 but i didint get the same answer as the calculator. Is it because that this method Is used for certain numbers?

[@chatzigeorgiougeorge885]

If the x (2.3) is further from your first guess (2), you need more terms in the linearization process. Or you use iterative techniques, like Newton-Raphson method.

[@stefangrothe7766]

2.3 if too far away from 2 for this method to work well.

[@cesarmoreno987y]

For April fools you should have made a video titled “use a calculator not calculus”

[@nanubhai7918]

16 i guess lol

[@justinbishop54]

2

[@BurningShipFractal]

2^4=16, or even 0, is okay, he said approximate, but didn’t say how accurate

[@finmat95]

Useless

[@zekecheng1339]

The awake jason optically hug because defense neurally kill beyond a trite forecast. thoughtful, pushy sister

[@Emblazon]

lim _{x -> 2} x⁴= 16 **fast approximation**

[@GodbornNoven]

I just found 2⁴ which is 16 and since (1.999)⁴