Evaluate the lim x-> infinity (-3x^4 - x^2 + 5)/(2x^5 - 7x^3)

Hey, Dibas. Don't worry buddy!

The process for doing this type of question where x approaches infinity is totally different than other questions where x approaches any real numbers like this question.

In this type of question, we should look at the values of the denominator which has the highest power of x or any variable depending on the questions. And then divide by that value which has the highest power in both the numerator and denominator.

After that, we just need to substitute the ∞ or -∞ in the expression and get our result.

= $lim_{x \, \to \, \infin} \frac{-3x^4 \, - \, x^2 \, + \, 5}{2x^5 \, - \, 7x^3}$

= $lim_{x \, \to \, \infin} \frac{\frac{-3x^4}{x^5} \, - \, \frac{x^2}{x^5} \, + \, \frac{5}{x^5}}{\frac{2x^5}{x^5} \, - \, \frac{7x^3}{x^5}}$

= $lim_{x \, \to \, \infin} \frac{\frac{-3}{x} \, - \, \frac{1}{x^3} \, + \, \frac{5}{x^5}}{2 \, - \, \frac{7}{x^2}}$

= $\frac{-0-0+0}{2-0}$

= 0