Question

lim x>0+ (1 + 3x/2)^1/x

Answer 1

gotta be \(e^{\text{something}}\) my guess is \(e^{\frac{3}{2}}\) since
\[\lim_{x\to 0}(1+x)^{\frac{1}{x}}=e\]

Answer 2

you have a choice here
one way it to take the log and get
\[\frac{1}{x}\ln(1+\frac{3x}{2})\] then take the limit of that using l'hopital, then exponentiate

Answer 3

second and actually correct (also equivalent way) is to write
\[(1+\frac{3x}{2})^{\frac{1}{x}}=e^{\frac{1}{x}\ln(1+\frac{3x}{2})}\] and then take the limit, but all with work will be identical

Answer 4

thanx.. the second one will probably work.. thanx so much

Answer 5

yw