Limits of functions are evaluated using many different techniques such as recognizing a pattern, simple substitution, or using algebraic simplifications. Some of these techniques are illustrated in the following examples.
Let ABC be a right angled triangle such that
Now , if we keep BC fixed and go on decreasing angle θ then we find that A goes on coming nearer and nearer to C
This means that
Consider a circle of radius r. Let O be the centre of the circle such that
where is measured in radians and it is very small . Suppose the tangent at A meets OB produced at P . From the below figure , we have