Pregunta: C) limx→∞5x2+2x2+32=

(c). Given, The limit is :$\underset{\mathrm{x}\to \mathrm{\infty }}{lim}\frac{5{\mathrm{x}}^2+2}{\sqrt{{\mathrm{x}}^2+3}}$
Multiply and divide by x :

$\underset{\mathrm{x}\to \mathrm{\infty }}{lim}\frac{5{\mathrm{x}}^2+2}{\sqrt{{\mathrm{x}}^2+3}}$=$\underset{\mathrm{x}\to \mathrm{\infty }}{lim}\frac{\mathrm{x}\frac{5{\mathrm{x}}^2+2}{\mathrm{x}}}{\mathrm{x}\frac{\sqrt{{\mathrm{x}}^2+3}}{\mathrm{x}}}$
Divide :

$\underset{\mathrm{x}\to \mathrm{\infty }}{lim}\frac{\mathrm{x}\frac{5{\mathrm{x}}^2+2}{\mathrm{x}}}{\mathrm{x}\frac{\sqrt{{\mathrm{x}}^2+3}}{\mathrm{x}}}$$=$$\underset{\mathrm{x}\to \mathrm{\infty }}{lim}\frac{5\mathrm{x}+\frac{2}{\mathrm{x}}}{\sqrt{1+\frac{3}{{\mathrm{x}}^2}}}$