Why do you investigate the limit value of a function closer and closer to a point, instead of just finding the value of a limit function at the point.

In some cases, finding the limit lets you find numbers simple solutions would't allow you to find. For example, with the equation (limit being x approaching 0), if you have the equation (x^2+1)/x, you can't plug 0 into the equation because you'd be dividing by 0. Finding the limit allows you to see the number approaching 0 even though you can't actually plug 0 into the equation.