# Limits

A number ‘l’ is called **limit** of a function f(x) when i.e., if given , there exists such that |x –a| | f(x) – l | < .

**Right hand and left hand limits**

Let h be a small positive number. Left hand side limit of f(x) when , is denoted by f(a -0) and is defined as:

**Right hand side limit** of f(x), when , is denoted by f(a + 0) and is defined as:

exists if

**Indeterminate forms**

If a **function** f(x) takes the form , then say that f(x) is indeterminate at x=a. Other Indeterminate Forms are .

**L’ hospital’s rule**

If and are **functions** of x such that , then

**The form **

This form can easily be reduced either to form of .

Example:

Evaluate

Solution:

**The form **

This can also be reduced to the form

Example:

Evaluate

**Sandwich Theorem (or Squeeze principle)**

If f, g, h are **functions** such that for all x in the neighborhood of a and if ,

**Algebra of limits**

,

**Evaluation of exponential limits of the form **

**Result**:

(i) If

(ii) If

Related posts:

- Partial Differentiation Defination of Partial Differentiation If f is a function...
- Continuity and Differentiability Definition of continuity at a point A function f(x)...
- Limit Formulas Limit and continuity Formulas Concept of limit and continuity was...
- Linear Differential Equations Linear Differential Equation of nth Order Linear differential equation is...
- Properties of Definite Integral Properties of Definite Integral Definite integral is part of integral...