Download NCERT Solutions for Class 11 Maths Chapter 13 Limits and Derivatives सीमा और अवकलज in PDF form free. All intermediate (class xi) students of CBSE, UP Board, MP Board, Gujrat Board, Uttarakhand Board and Bihar board, who are using NCERT Books as their course books, can use there solutions. NCERT Solutions of other subjects are also given to download free without any login and password.
Table of Contents
NCERT Solutions for Class 11 Maths Chapter 13
Class 11 Maths Chapter 13 Limits and Derivatives Sols
- Download Exercise 13.1
- Download Exercise 13.2
- Download Miscellaneous Exercise 13
- Download Supplementary Exercise 13.2
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- Hindi Medium Solutions will be uploaded very soon.
- Limits: Meaning of x approaches (x->a): Let x be a variable and ‘a’ be a fixed number. If x assumes a succession of values nearer and nearer to ‘a’, it is said to approach ‘a’. We mean that x assumes successively values [neither greater nor less than a] there is no end to this process of coming nearer and nearer to ‘a’. In this process (x – a) becomes smaller and smaller and can be made as small as we like. We express this by saying that |x – a| become smaller than δ, where δ is an arbitrary number which may be as very small as we please.
- Definition of x ->a: Let x be a variable and ‘a’ be a fixed number. Given a positive number δ however small it may be, if x assumes values such that 0 < |x – a| < δ, then we say x tends to ‘a’ and write x ->a.
- Concept of Limit: Let any function f(x) = y, is not defined at x = a, then the value of function at x = a is f(a), is meaningless. In this case the value of x can be taken nearer to a. Then the value of f(x) is calculated at that nearer value. Hence, the value of f(x) nearer to a. This limiting value of f(x) is known as limit of x.