Use properties of Logarithms to simplify the limit:
[tex]\lim_{x \to \0^+}[/tex]e^3/x(e^x+x)
Move the limit to the exponent:
e^x[tex]\lim_{x \to \0^+}[/tex]3/xln(e^x+x)
Rewrite as:
e^x[tex]\lim_{x \to \0^+}[/tex]3ln(e^x+x)/x
Move 3 outside the limit and applay L'hospitals rules to get the final answer e^6
