In the above way, when x tends to infinity, both the numerator and denominator tend to infinity. Take the derivative of the numerator and denominator twice, and you can know that the limit value is 0.

In the following way, when x tends to infinity, both the numerator and denominator tend to 0. Take the derivative of the numerator and denominator, the numerator is 6x 5+8 and the denominator is e x.

The limit is 8.