Question

\[\lim_{x \rightarrow 0} ( 1+x+f(x)/x) ) ^{1/n} = e^3\] then find \[\lim_{x \rightarrow 0} \frac{ f(x) }{ x^2}\]

Answer 1

@hartnn @RadEn @Coolsector

Answer 2

Try by taking log of both sides of equation.

Answer 3

*tried...no result

Answer 4

mmm I thing there is no result sice limit of 1/x is not exist ... retype the qs again

Answer 5

log (1+x+f(x)/x)=3x..solve for f(x).

Answer 6

Using L'Hospital's rule you get that the log term must be of order 3x.

Answer 7

ok i think you well goes like this\[(\lim 1+x+\frac{ f(x) }{ x } )^\frac{ 1 }{ n }= e^3 \]
\[\lim 1+x+\frac{ f(x) }{ x } = e^3n \]
\[\lim \frac{ f(x) }{ x } = e^3n -1\]

Answer 8

oh i thought the n was x..sorry for that :(

Answer 9

ya i thouth it x at first too

Answer 10

lol...Sorry it is x

Answer 11

not n...:(

Answer 12

huh ... mmm use the log as @quarkine showed

Answer 13

but not log take ln

Answer 14

yep i meant ln too.in math i guess we almost never bother with base 10!

Answer 15

@satellite73 @bahrom7893

Answer 16

@Mertsj