use calculus to approximate 1.999^4 (no calculators)

Рет қаралды 14,610

2 жыл бұрын

Use calculus to approximate 1.999^4 (no calculators).
We will use local linear approximation to approximate 1.999^4 and we will also use differential to do the same. This is a calculus 1 homework problem from James Stewart's Single Variable Calculus textbook.
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Пікірлер: 37

@DrBarker 2 жыл бұрын

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 2 жыл бұрын

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

@kobethebeefinmathworld953 2 жыл бұрын

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.

@ChristAliveForevermore 2 жыл бұрын

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

@jamescollier3 2 жыл бұрын

forest trees

@geraltofrivia9424 2 жыл бұрын

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.

@teelo12000 2 жыл бұрын

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 2 жыл бұрын

lol

@helgen3821 2 жыл бұрын

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

@nick46285 2 жыл бұрын

not accurate enough without calculus

@evanlawrence 2 жыл бұрын

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

@sleepingboiz8155 2 жыл бұрын

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

@user-zt4hf2eu6g 2 жыл бұрын

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 2 жыл бұрын

Yup

@flowers42195 2 жыл бұрын

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

@NoNameAtAll2 2 жыл бұрын

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

@VincentCSPG3D 2 жыл бұрын

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

@carlossecas2756 10 ай бұрын

great explanation

@fernandofa2001 2 жыл бұрын

Very interesting!

@yaskynemma9220 2 жыл бұрын

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 2 жыл бұрын

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 2 жыл бұрын

Ah yes. That would have been much better

@nanubhai7918 2 жыл бұрын

16 i guess lol

@beabzk 2 жыл бұрын

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

@user-wu8yq1rb9t 2 жыл бұрын

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

@lekanakinwale8411 2 жыл бұрын

Using binomial theorem to approximate>>>

@justinbishop54 2 жыл бұрын

@Anti_Electron 2 жыл бұрын

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 2 жыл бұрын

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 жыл бұрын

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