Calculus Limits Explained

If you are having a problem understanding Calculus limits, then this Calculus Limits Explained will help you learn what calculus limits are and how to solve some calculus limit problems.

The Idea of Limits

The idea of a limit in Calculus can be quite ambiguous and confusing. Limit is also called limiting value. The idea of a limit comes from defining tangent of a curve. The tangent to a curve at a point A can be described as a line that:

1. touches the curve at A
2. has two coincident points of intersection with the curve at A, or
3. is the limiting position of a chord AB as B approaches A

So, the closer B is to A, the closer it is to the tangent of the curve. When you have no idea what the tangent of the curve is, it is helpful to be able to say that it is the Limit of the curve at the point where B approaches A. Then you can begin to solve the problem and find the tangent of the curve.

Illustration that will help you understand Limits

Suppose, the function above is f(x) = y = x² and we want to find the equation of its tangent at point (1,1). Using method #3 (limiting method) listed above, we let the coordinate of B be (x,y) so the slope of line AB is (y-1)/(x-1). by substituting y for x, we get:

Slope of AB is = (x² -1)/(x-1)

We also know that the coordinate B must satisfy f(x)=x²  because it is only on the slope. If we give x some values that are closer and closer to x=1 such as x=1.1, 1.01, 1.001, etc, then we find that the value of the slope gets closer and closer to 2. That means the limiting value or the limit of the slope AB is 2.