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Introduction

Limit and Derivative of Class 11

Definition (Limits)

Let f(x) be a function of x. If for every positive number ∈ there exists a positive number δ, such that 0 < |x-a| < δ we have.

|f(x) – l| < ∈ then we say

f(x) tend to limit l as x tend to a and we write limitsf (x) = l.

Right Hand And Left Hand Limits

In the definition of the limit we say that l is the limit of f(x) if f(x) → l when x → a.

If we modify the definition a little further that is when x → a from the values of x > a then the corresponding limit is called the RHL (Right Hand Limit) of f(x) and is written as

limits

Or in short f(a+0) = limits

Like wise f(a-) = limits is said to be the Left Hand Limit LHL).

If both the limits exist i.e. finite and are equal to each other than the function is said to have a definite limit.

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