Problem 3.3

Verify the following limits. $\lim_{s\rightarrow 1} \frac{s^3-1}{s-1} =3$

$\lim_{\theta \rightarrow 0} \frac{1-\textrm{cos} \theta }{\theta ^2} =\frac{1}{2}$

$\lim_{x \rightarrow \infty} \frac{5x^2-2x }{x} =\infty$

$\lim_{n \rightarrow \infty} \frac{n(n+1)}{(n+2)(n+3)} =1$

$\lim_{x \rightarrow \infty} \frac{ax^2+bx+c}{dx^2+ex+f} =\frac{a}{d}$

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