CBSE Class 11 Maths Notes Chapter 13 Limits and Derivatives

Limit
Let y = f(x) be a function of x. If at x = a, f(x) takes indeterminate form, then we consider the values of the function which is very near to a. If these value tend to a definite unique number as x tends to a, then the unique number so obtained is called the limit of f(x) at x = a and we write it as $\lim _{ x\rightarrow a }{ f(x) }$ .

Left Hand and Right-Hand Limits
If values of the function at the point which are very near to a on the left tends to a definite unique number as x tends to a, then the unique number so obtained is called the left-hand limit of f(x) at x = a, we write it as
Limits and Derivatives Class 11 Notes Maths Chapter 13 1

Existence of Limit
Limits and Derivatives Class 11 Notes Maths Chapter 13 2

Some Properties of Limits
Let f and g be two functions such that both $\lim _{ x\rightarrow a }{ f(x) }$ and lim $\lim _{ x\rightarrow a }{ g(x) }$ exists, then
Limits and Derivatives Class 11 Notes Maths Chapter 13 3

Some Standard Limits
Limits and Derivatives Class 11 Notes Maths Chapter 13 4

Derivatives
Suppose f is a real-valued function, then
Limits and Derivatives Class 11 Notes Maths Chapter 13 6

Fundamental Derivative Rules of Function
Let f and g be two functions such that their derivatives are defined in a common domain, then
Limits and Derivatives Class 11 Notes Maths Chapter 13 7

Some Standard Derivatives
Limits and Derivatives Class 11 Notes Maths Chapter 13 8

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CBSE Class 11 Maths Notes Chapter 13 Limits and Derivatives