Ale

my name is Alejandro, I'm 22, I'm from Chile and I study math engineering.

we just need this little fact: [math]\underset{x\to 0}{\mathop{\lim }}\,x\ln x=0,[/math] thus [math]x^{\sin x}=\exp (\sin (x)\ln x)=\exp \left( \frac{\sin x}{x}\cdot x\ln x \right)\to 1[/math] as [math]x\to0.[/math]