Calculate the limit algebraically and does the limit exist?

Question

lim  4x^2+5x+50/ 2x^2-4

x→−∞

Answer 1

ASSUMING you mean (4x^2 +5x+50)/(2x^2 -4)

Dividing them:

2 + (5x+58)/(2x^2-4)

as x-->infinity, the remainder fraction vanishes,

so the limit is 2