Question

Lim 5 x16-3x4+2
x ⇒ - ∞ 7x16-2x8+4x


Lim 2x3+x2+1
x ⇒ ∞ 16x15+2x9+1

Answer 1

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

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