Determine the given limit without any simplification. If the limit limit goes through or $$$,$ state this answer.

lim$$x$$$4$x$2+3$

Evaluate the limit if it exists. $($If an answer does not exist, enter DNE.$)$

State the reason for the answer of the limit$.$

The limit goes to infinity because the highest exponent is in the numerator. The limit is the ratio of the coefficients with the same highest exponent.$$ The limit goes to $0$ because the higher exponent is in the denominator. Plug in the number and limit goes to a finite number. Simplify the expression to remove the discontinuity. Then take the limit by plugging in the number