Question

Вычислите предел фунцкии:
lim ->∞ (4-x^3+x^5)/(2x^5+x-3)

Answer 1

$\lim_{x \to \infty} \frac{4-x^3+x^5|:x^5}{2x^5+x-3|:x^5}=|\frac{\infty}{\infty}|=\lim_{x \to \infty}\frac{\frac{4}{x^5}-\frac{x^3}{x^5}+\frac{x^5}{x^5} }{\frac{2x^5}{x^5}+\frac{x}{x^5}-\frac{3}{x^5}}=\lim_{x \to \infty}\frac{\frac{4}{x^5}-\frac{1}{x^2}+1 }{2+\frac{1}{x^4}-\frac{3}{x^5}}=\frac{0-0+1}{2+0-0}=\frac{1}{2}.$