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Pepsi [2]
3 years ago
14

If f'(x)=2/x and f(sqrt(e))=5, then f(e)=

Mathematics
1 answer:
docker41 [41]3 years ago
3 0
f'(x)=\dfrac2x
\implies f(x)=\displaystyle\frac2x\,\mathrm dx=2\ln|x|+C

f(\sqrt e)=5\implies 5=2\ln|\sqrt e|+C
\implies 5=\dfrac22\ln e+C
\implies C=4
\implies f(x)=2\ln|x|+4
\implies f(e)=2\ln|e|+4=6
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