The horizontal asymptote of a function is a straight line in which the value of the function also approaches a certain value when the independent variable approaches a certain value. There are several main ways to solve horizontal asymptote:
1.Direct solution: For a function of the form y=f(x), if there is a real number a, when x a, if the limit of f(x) exists and is finite, then the straight line y=f(a) is the horizontal asymptote of the function.
2.Factorization: For a function of the form y=f(x), if it can be decomposed into y=g(x)h(x), where g(x) and h(x) are both derivatives, and g(a)=0 or h(a)=0, then the straight line y=g(a)h(b) is the horizontal asymptote of the function, where b is the real number such that h(b)=0.
3.Rationalization: For a function of the form y=f(x), if it can be rationalized so that the numerator and the denominator are equal, then the straight line y=0 is the horizontal asymptote of the function.
It is important to note that the horizontal asymptote of the function may have multiple or even non-existent lines. In the process of solving, it is necessary to select the appropriate method for analysis according to the specific form and characteristics of the function.