Why are they looking for the asymptote in this way?

Question

Mathematics

To search for the oblique asymptote, first look for the limit x strem. to endless function is divided by x. The question is why? Why coef. k asymptotes get like this? Same thing about finding coef. b.

Answer 1

The asymptote is the line towards which the function tends. How to find it? Find tangents. If the tangents tend to one, then this is an asymptote. It remains only to find this tangent. In our case, it is a straight line. Hence, it can be expressed through y=kx+b, where k is the limit of the derivative.