A problem on limit involving various functions Find the value of $$\lim \limits_{x\to 0} \frac{\tan\sqrt[3]x\ln(1+3x)}{(\tan^{-1}\sqrt{x})^2(e^{5\large \sqrt[3]x}-1)}$$
Applying L'Hospital's rule does not seem to simplify the expression.

If you change variable (x = y^3) and expand as a Taylor series at y=0, the first terms are   3/5 - 3 y / 2 + 29 y^2 / 20 +...
