#Can someone explain how they simplified this?

23 messages · Page 1 of 1 (latest)

winged portal
dusty isle
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I've never seen someone explain limit like that

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it is quite confusing

winged portal
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here's some of the explanation

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but it's still a little confusing

winged portal
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are they comparing the highest degrees of each the nominator and the denominator?

dusty isle
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for polynomial divided by polynomial, we can do that

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only for polynomial devided by polynomial, I emphasize

winged portal
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got it

dusty isle
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Lemme show an approach you may be interested

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$$\lim_{x \to \infty} \frac{6x\log x + 5x -2}{2^x \mp 2x - 14\log x} = \lim_{x \to \infty} \frac{\frac{6x \log x}{2^x} + \frac{5x}{2^x} -\frac{2}{2^x}}{ 1 -\mp \frac{2x}{2^x} - \frac{14\log x}{2^x}} = \frac{0}{1} = 0$$

wooden pulsarBOT
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k12byda5h

627803521051262986.png
dusty isle
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because 2^x grows faster than xlogx, x, logx etc

weak mountain
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Ye

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I think the main idea here is just the 'speed'

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And the solution in this image is using some very 'personal trick'

winged portal
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Yeah they were talking about the growth rate

weak mountain
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TBH, it's strange to write like this. Hhahaa