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slava [35]
3 years ago
7

30 POINTS!!! HELP!!!!

Mathematics
1 answer:
Lemur [1.5K]3 years ago
7 0
I think its f(0) = 3
Thats the only one that sounds true but not sureee
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Answer:

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6 0
3 years ago
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Not sure how to approach this one, any help would be appreciated!
iren2701 [21]
The continuity of f' and its limiting behavior guarantees that f' is Riemann integrable, so you can write

\displaystyle\int_0^\infty f'(x)\,\mathrm dx=uv\bigg|_{x=0}^{x\to\infty}-\int_0^\infty v\,\mathrm du

where u=1\implies\mathrm du=0\,\mathrm dx and \mathrm dv=f'(x)\,\mathrm dx\implies v=f(x), so that

\displaystyle\int_0^\infty f'(x)\,\mathrm dx=f(x)\bigg|_{x=0}^{x\to\infty}=\lim_{x\to\infty}f(x)-f(0)=-f(0)
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