Calculating Limit as x Approaches Infinity

[Guest2]

I'm trying to find $\displaystyle \lim_{x \to 20^{+}}\frac{5x^3+1}{20x^3-8000x}$

$\displaystyle \lim_{x \to 20^{+}}\frac{5x^3+1}{20x^3-8000x} =\lim_{x \to 20^{+}}\frac{5+1/x^3}{20-8000/x^2} = \frac{5+\lim_{x \to 20^{+}}1/x^3}{20-\lim_{x \to 20^{+}}8000/x^2} = \frac{5+\frac{1}{8000}}{20-\frac{8000}{400}} = \infty. $

I'm not sure because it seems I have a zero dominator throughout.

 

[evinda]

$\displaystyle \lim_{x \to 20^{+}}\frac{5x^3+1}{20x^3-8000x}$

Since $5\cdot 20^3+1>0, 20 \cdot 20^3-8000 \cdot 20=0$ and we approach $20$ from the right side, we can immediately say that $\displaystyle \lim_{x \to 20^{+}}\frac{5x^3+1}{20x^3-8000x}=+\infty$.