Question

what is the limit as x approaches infinity for 5x^4+3x^2+1/x-7x^4

Answer 1

divide each term by the highest power of x

so divide every term by x^4

\[\frac{5 +3/x^2 +1/x^4} {-7 + 1/x^3}\]

now as x approaches infinity 1/x^n approaches zero

so \[\lim_{x \rightarrow \infty} \frac{5x^4 +3x^2 +1}{x-5x^4} = -\frac{5}{7}\]

Answer 2

or you can use L'Hospital's Rule. Differentiate until 120/-168 or 5/-7