convergent or divergent (three improper integrals)

[TYSONG]

I am needing to figure out whether these problems are convergent or divergent can anyone help me?

 

[pka]

Your first two depend on: \(\displaystyle p > 1\quad \Rightarrow \quad \lim _{n \to \infty } \int\limits_a^n {\frac{{du}}{{u^p }}} = \lim _{n \to \infty } \left[ {\frac{1}{{\left( {p - 1} \right)a^{p - 1} }} - \frac{1}{{\left( {p - 1} \right)n^{p - 1} }}} \right] = \frac{1}{{\left( {p - 1} \right)a^{p - 1} }},\quad (a > 0)\)

The third depends upon knowing \(\displaystyle \lim _{n \to \infty } e^{ - n} = 0\)