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# Limits and derivatives

Limits are used when we have to find the value of a function near to some value.

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      Tags : Definition, Formula, Solved Example Problems, Exercise | Differential Calculus | Mathematics , 11th Business Mathematics and Statistics(EMS) : Chapter 5 : Differential Calculus
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11th Business Mathematics and Statistics(EMS) : Chapter 5 : Differential Calculus : Limits and derivatives | Definition, Formula, Solved Example Problems, Exercise | Differential Calculus | Mathematics