Proof Question - unknown school trial (1 Viewer)

gamja · Jul 27, 2023

i) was fine. However, I'm stuck on reconciling an e function with the rest of the inequality for ii).

Thanks in advance for your help!

cossine · Jul 27, 2023

gamja said:
View attachment 39094

i) was fine. However, I'm stuck on reconciling an e function with the rest of the inequality for ii).

Thanks in advance for your help!

ii reminds me of bernoulli inequality. But I am not sure if that is the way

tywebb · Jul 27, 2023

$\textstyle\frac{1}{4}\ge\frac{x}{x^2+4}$
$\textstyle\int_0^\alpha\frac{1}{4}dx\ge\int_0^\alpha\frac{x}{x^2+4}dx$
$\textstyle[\frac{1}{4}x]_0^\alpha\ge\frac{1}{2}\int_0^\alpha\frac{2x}{x^2+4}dx=\frac{1}{2}[\ln(x^2+4)]_0^\alpha$
$\textstyle\frac{1}{4}\alpha\ge\frac{1}{2}\ln\frac{\alpha^2+4}{4}$
$\textstyle\frac{1}{2}\alpha\ge\ln(\frac{\alpha^2}{4}+1)$
$\textstyle e^{\frac{1}{2}\alpha}\ge\frac{\alpha^2}{4}+1$

synthesisFR · Jul 27, 2023

Screen Shot 2023-07-27 at 8.19.36 pm.png

hornsby told u the method to use

Proof Question - unknown school trial (1 Viewer)

gamja

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cossine

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tywebb

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