What is the value of [math] \displaystyle \lim_{x \to 0} \frac{\sin^2 (x)}{\sqrt{1+x \sin x} - \cos x} [/math]?
What is the value of [math]\lim_{x\to\infty} \left( \left (\frac{x}{x+1} \right) ^{a} + \sin \frac{1}{x} \right) ^{x}[/math]?