Method 1: directly calculate f(x) by partial integration, and then judge the extreme value.

Method 2: Because f(x) is continuously differentiable everywhere in the definition domain, the derivative can be directly obtained, so that the point of x= 1 can be obtained by making the derivative 0.

Question 2: Using the four operations of limit, the limit of the first part is 2, because tanx-x (x-0) and the limit of the latter part is 0, because sinx is a bounded function and 1/(x*x) is infinitesimal, so the multiplication of the two is infinitesimal, and then the limit is 0.

These are the basic problems in advanced mathematics.