A great question for math lovers

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Күн бұрын

What do you think about this problem? If you're reading this ❤️.
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Пікірлер: 22

@SidneiMV Ай бұрын

2ˣ = x x2⁻ˣ = 1 -x2⁻ˣ = -1 (-xln2)e⁻ˣˡⁿ² = -ln2 (-xln2)e⁻ˣˡⁿ² = ln(1/2) W[(-xln2)e⁻ˣˡⁿ²] = W[ln(1/2)] -xln2 = W[ln(1/2)] *x = W[ln(1/2)]/ln(1/2)*

@ZannaZabriskie Ай бұрын

Very complicated method. Interesting but complicated. You can solve it with mental arithmetic. Two simple considerations: 1. y=2^x and y=x are continuous and monotonic functions, theirs derivatives too. 2. When x-> +-oo 2*x > x In theese conditions you have one and only one point in which the derivative of 2^x is 1, the derivative of x: if in this point 2^x < x You have two intersections. If 2^x > x You have NO intersection point. Now you have only to find the point, evaluate and compare the two functions. (Actually for the evaluation (only) I used calculator 😅)

@benyseus6325 Ай бұрын

You would need to specify at start of problem that x∈C to not confuse the students.

@ericerpelding2348 Ай бұрын

Can this be solved without using the W function?

@tmjcbs Ай бұрын

Not algebraically, only by approximation...

@ZannaZabriskie Ай бұрын

Yes. Functions and their derivative are monotonic. Look at the graph and you understand.

@cheesefrogsnail Ай бұрын

You don't need the W function to find there no solution in R, just study the fonction 2^x-x

@RichardPerusse Ай бұрын

Draw the graphs of y=x and y=2^x and it is clear from the start that those two functions do not not intersect Also (ln x/x) reaches its maximum of (1/e) at x=e and cannot reach ln 2. So, no real solution.

@wilsonpereira1307 Ай бұрын

The solution seems a bit "forced".

@keescanalfp5143 Ай бұрын

& what about the problem .

@gnanadesikansenthilnathan6750 Ай бұрын

Can we apply differentiation?

@Dzevad75 Ай бұрын

x≈0.5

@duckyoutube6318 Ай бұрын

No. That would mean 2^1/2=1/2 but 2^1/2=srt(2).... not 1/2

@irenehartlmayr8369 Ай бұрын

Pronunciation please.....its " natural " and NOT " naytural ".....!!!!!

@hugoprince868 Ай бұрын

I feel like it's just his accent, so I don`t really understand why it's so important

@moebadderman227 Ай бұрын

He is not to blame for the inconsistency of English pronunciation. nature = "nayture" and natural = "nahtural"

@irenehartlmayr8369 Ай бұрын

@@moebadderman227 Well,he is obviously not to blame for the inconsistency of English pronunciation but,in a video of quality,I think that the correct pronunciation is also a matter that should be considered.A consistent mispronunciation of a recurring word can be corrected. And should be.

@irenehartlmayr8369 Ай бұрын

@@hugoprince868 Its disturbing to a musical ear. Particularly if repeated again and again...