Find out the value of n if the limit lim [ln(1+nx)]/x=3 and x tends to 0.

giorgiana1976 | Student

lim [ln (1+nx)]/x=lim (1/x)*ln(1+nx)=lim ln(1+nx)^(1/x)=

ln lim (1+nx)^(1/x) = ln lim [(1+nx)^(1/nx)]*n=ln e^n=n*ln e=n

But, from hypothesis, lim [ln (1+nx)]/x=3, so n=3

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