Question

Lim 5 x16-3x4+2 x ⇒ - ∞ 7x16-2x8+4x lim 2x3+x2+1 x ⇒ ∞ 16x15+2x9+1

Answer 1

$\lim_{x \to \infty} \frac{5x^{16}-3x^4+2}{7x^{16}-2x^8+4x} = \dfrac{5- \frac{3}{x^{12}} + \frac{2}{x^{16}} }{7- \frac{2}{x^8}+ \frac{4}{x^{15}} } = \frac{5-0+0}{7-0+0} = \frac{5}{7}$

$\lim_{x \to \infty} \frac{2x^3+x^2+1}{16x^{15}+2x^9+1} = \lim_{x \to \infty} \frac{ \frac{2}{x^{12}}+ \frac{1}{x^{13}}+ \frac{1}{x^{15}} }{16+ \frac{2}{x^6}+ \frac{1}{x^{15}} } =0$