Limits and derivatives

Limits and derivatives

In this section, we will discuss about limits, continuity of a function, differentiability and differentiation from first principle. Limits are used when we have to find the value of a function near to some value.

1. Existence of limit

2. Algorithm of left hand limit : L[f(x)]x=a

3. Algorithm of right hand limit : R[f(x)]x=a

4. Some results of limits

5. Indeterminate forms and evaluation of limits

6. Methods of evaluation of algebraic limits

1.     Direct substitution

2.     Factorization

3.     Rationalisation

4.     By using some standard limits

7. Some standard limits

Derivative

Before going into the topic, let us first discuss about the continuity of a function. A function f(x) is continues at x = a if its graph has no break at x = a

If there is any break at the point x = a then we say that the function is not continuous at the point x = a.

If a function is continuous at all the point in an interval, then it is said to be a continuous in that interval.

8. Continuous function

9. Some properties of continuous functions

10. Differentiability at a point

11. Left hand derivative and right hand derivative

12. Differentiation from first principle

13. Derivatives of some standard functions using first principle