find the limit. (if the limit is infinite, enter \\( \\infty \\) or \\( -\\infty \\), as appropriate. if the…
find the limit. (if the limit is infinite, enter \\( \\infty \\) or \\( -\\infty \\), as appropriate. if the limit does not otherwise exist, ent\n\\ \\lim _{x \\rightarrow-\\infty} \\frac{3 x^{5}-x}{x^{4}+4} \\
Answer
Explanation:
Step1: Divide numerator and denominator by (x^4)
$$\lim_{x\to -\infty}\frac{3x^5 - x}{x^4 + 4}=\lim_{x\to -\infty}\frac{\frac{3x^5}{x^4}-\frac{x}{x^4}}{\frac{x^4}{x^4}+\frac{4}{x^4}}=\lim_{x\to -\infty}\frac{3x-\frac{1}{x^3}}{1 + \frac{4}{x^4}}$$
Step2: Evaluate the limit
As (x\to-\infty), (\frac{1}{x^3}\to0) and (\frac{4}{x^4}\to0). So the limit becomes (\lim_{x\to -\infty}(3x)) Since (x\to-\infty), (3x\to-\infty)
Answer:
(-\infty)