0Maths is often taught mechanically. Just consider the case of limits. Most of the standard textbooks define, the limit is the value that a function "approaches" as the input "approaches" some value.
This neither gives the "feel" of maths, nor a beginner can appreciate its "beauty". A graphical approach is often more insightful.
Consider, the graph of f(x)=1/x.
In this case, at X=0, the value of f(x) approaches minus infinity if we approach from the negative side of the number line and f(x) approaches plus infinity if we approach from the positive side of the number line. Essentially, the limit doesn't exist as LHL is minus infinity and RHL is plus infinity.
Now to make it more clear consider the graph of f(x)=1/x^2
Here at x=0, both LHL and RHL approaches plus infinity. Hence limit exists as plus infinity at x=0.
Just by observing these two graphs a beginner gets an insight into when a limit is said to exist and when not.
