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.

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**1. Existence of limit**

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

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

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**4. Some results of limits**

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**5. Indeterminate forms and evaluation of limits**

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**6. Methods of evaluation of algebraic limits**

1. Direct substitution

**2. **Factorization

3. Rationalisation

4. By using some standard limits

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**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.

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**8. Continuous function**

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**9. Some properties of continuous functions**

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**10. Differentiability at a point**

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**11. Left hand derivative and right hand derivative**

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**12. Differentiation from first principle**

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**13. Derivatives of some standard functions using first principle**

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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