CALCOLO DI LIMITI CON GLI SVILUPPI DI TAYLOR

$\underset{x\to 0^{+}}{lim}\frac{x^2\tan x-{\left(\sin x\right)}^3}{{\left(1+x^5\right)}^2-x·\cos x-1+x-\frac{x^3}{2}}$
$\underset{x\to +\infty }{lim}[e^{\frac{x^2}{1+x}}-{\left(1+\frac{1}{x}\right)}^{x^2}]$
$\underset{x\to 0^{+}}{lim}\frac{\frac{1}{2}x·\sin x+\ln \left(1+x\right)-x}{x^{2+x}-x^2}$
$\underset{x\to 0^{+}}{lim}\frac{2\left(x-1\right)\cos x+x^3-x^2-2x+2}{x^3{e}^x(x^2+1)\sin x}$
$\underset{x\to 0}{lim}\frac{2\left(1-\cos x\right)\sin x-x^3}{{\left(\sin x\right)}^3-x^3}$