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### Limits and Continuity-cbse mathematics

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**Introduction**

**Limit and continuity is the introduction of calculus. Calculus is
that branch of Mathematics which mainly deals with the study of change in the
value of a function as the point in the domain changes.**

**Definition: **

**Suppose f is a real function on a subset of the real numbers and
let c be a point in the domain of f. Then f is continuous at c
if **

**ALGEBRA OF LIMITS**

**Undefined terms:**** **

** all these terms are called undefined terms**

__IMPORTANT FORMULAS USED IN LIMITS__

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**Left Hand Limit and Right Hand Limit**

If at any point c given function have two different values then at that point (c) we calculate LHL and RHL. and the limit exist if

Left Hand Limit = Right Hand Limit = f(c)

LHL is denoted by

RHL is denoted by

When limit exist then

For a function f(x) the limits and may or may not exist

If both limits and exist, they may not be equal.

If then does not exist

If , then exist and is equal to the common limit.

A function is said to be continuous if its limit exist or if or if

Left Hand Limit = Right Hand Limit = f(c)

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EVERYWHERE CONTINUOUS FUNCTIONThere were some functions which are always continuous in their domain. The functions which are given below are always continuous in their domain

Constant Functions

Exponential Functions

Polynomial Functions

Modulus Functions

Rational Functions

Trigonometric Functions

Logarithmic Functions

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__Some other formulas used in limits__**EXPONENTIAL LIMITS**

Here we use the series

__LOGARITHMIC LIMITS__** **

**Here we use the series:**

** **

, where a > 0

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