Calculus is interested in motion and change of quantities that depend on certain parameters through a rule. For example, the change of velocity of a car with respect to time, change in temperature with respect to the temperature of the surrounding environment, growth of a certain amount of money with respect to interest rate are only a few that comes to mind.

It has two fundamentally significant concepts.The first of these concepts is the derivative, that is finding instantaneous change of a given function at a given point. It corresponds to the problem of finding the slope of a line tangent to a given curve at a given point on the curve. The second problem is concerned with finding the area of a plane region bounded by given curves. The solution of the problem of areas is the subject of the integral concept. 

Suppose that a ball is dropped from the top of a tower of height 200m. In the first t seconds, the distance of the ball travels is given by the equation
y (t)= 4,9t².

The tangent line problem is the problem of finding a line that is tangent to a given curve (circle, graph of any function, etc.) at a given point P on the curve.

Let us note that the expression ‘’x?x₀’’ in the definition of limit means that even though f may not be defined at the point x₀, we can make the value of f (x) as close as we want to L.

The limit of a function at a given point x₀ determines the behaviour of the function near x₀.

The symbols –? and +? do not represent numbers. They imply unbounded behaviour.

If a function f is continuous at every point of the interval I, where it is defined, we say that f is continuous on the interval I. Also, if f is continuous at every point of its domain of definition, we say that f is a continuous function.