Manim test - (sort of) proof of limit sin x / x

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  1. MATH RMUTP
  2. mathematics
  3. educational
  4. undergraduate course
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You can get great visual understanding of this when trying it out on desmos. If you zoom in far enough, you'll see (of course) that y = sin(x) becomes more and more like y = x, close to origo.

PingSharp
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The very first triangle is wrong. It should be a scalene triangle with the bottom right point on the circumference. THEN the area would be 1/2 * base * height = 1/2 * 1 (unit circle) * sin x = (sin x) / 2.

reedrichmeier
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What's the point of flipping all elements if the order of equality stays the same? 0:23

ianthehunter
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Sir, what is use/applicablilty of this solved expression, plz suggest me

SurinderKumar-osil
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sinx = x for small x
0 is small
x/x = 1

yante
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I'm familiar with that proof but I don't like it. I mean sinx tends to 0 when x tends to 0. So, sinx/x is actually similar to 0/0 which tends to infinity. Right?

pelasgeuspelasgeus