sumaewill
sumaewill
17-04-2017
Mathematics
contestada
If f'(x)=2/x and f(sqrt(e))=5, then f(e)=
Respuesta :
LammettHash
LammettHash
17-04-2017
[tex]f'(x)=\dfrac2x[/tex]
[tex]\implies f(x)=\displaystyle\frac2x\,\mathrm dx=2\ln|x|+C[/tex]
[tex]f(\sqrt e)=5\implies 5=2\ln|\sqrt e|+C[/tex]
[tex]\implies 5=\dfrac22\ln e+C[/tex]
[tex]\implies C=4[/tex]
[tex]\implies f(x)=2\ln|x|+4[/tex]
[tex]\implies f(e)=2\ln|e|+4=6[/tex]
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