How do you evaluate  (7r + 3)/(5r^2 - 2r + 2)  as r approaches infinity?

Jun 21, 2016

$0$

Explanation:

As we see, the highest power in the whole fraction is 2 (in $5 {r}^{2}$), so we divide both numerator and denominator by ${r}^{2}$

$\frac{\left(\frac{7}{r}\right) + \left(\frac{3}{r} ^ 2\right)}{5 - \left(\frac{2}{r}\right) + \left(\frac{2}{r} ^ 2\right)}$

As r approaches infinity, $\frac{1}{r}$ approaches zero

Hence, substituting 0 for $\frac{1}{r}$, we get

$\frac{0 + 0}{5 - 0 + 0}$

This becomes $\frac{0}{5}$ which is $0$

Hence the answer is $0$