NCERT Solutions for Class 11 Maths Chapter 13

NCERT Solutions for Class 11 Maths Chapter 13 Limits and Derivatives Seema Aur Avkalan in PDF format free to download updated for new academic session 2020-21 based on latest NCERT Books 2020-2021.

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NCERT Solutions for Class 11 Maths Chapter 13

Class:11
Subject:Maths
Chapter 13:Limits and Derivatives

11th Maths Chapter 13 Solutions

NCERT Solutions for Class 11 Maths Chapter 13 Limits and Derivatives given below to use free online or download in PDF form for new academic session 2020-21. Join the Discussion Forum to discuss your doubts related to education and study.




Important Terms Related to Limits & Derivatives

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.

Concept of Limit

1. 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.
2. 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.



Important Questions on 11th Maths Chapter 13

Evaluate the Given limit: lim(x→3)⁡:〖x+3〗
lim (x→3):⁡〖x+3〗
= 3 + 3
= 6
Find the derivative of x^n+ax^(n-1)+a^2 x^(n-2)+⋯+a^(n-1) x+a^n for some fixed real number a.
Let f(x)=x^n+ax^(n-1)+a^2 x^(n-2)+⋯+a^(n-1) x+a^n
∴f^’ (x)=d/dx(x^n+ax^(n-1)+a^2 x^(n-2)+⋯+a^(n-1) x+a^n)
=d/dx (x^n )+a d/dx (x^(n-1) )+a^2 d/dx (x^(n-2) )+⋯+(a^(n-1 ) d)/dx (x)+a^n d/dx (1)
On using theorem d/dx x^n=nx^(n-1) ,we obtain
f^’ (x)=nx^(n-1)+a(n-1) x^(n-2)+a^2 (n-2) x^(n-3)+⋯+a^(n-1)+a^n (0)
=nx^(n-1)+a(n-1) x^(n-2)+a^2 (n-2) x^(n-3)+⋯+a^(n-1)
Find the derivative of the following functions (it is to be understood that a,b,c,d,p,q,r and s are fixed non-zero constants and m and n are integers): (px+q)(r/x+s).
Let f(x)=(px+q)(r/x+s)
f'(x)=(px+q) (r/x+s)’+(r/x+s) (px+q)’
=(px+q) (rx^(-1)+s)’+(r/x+s)(p)
=(px+q)(-rx^(-2) )+(r/x+s)p
=(px+q)((-r)/x^2 )+(r/x+s)p
=(-pr)/x-qr/x^2 +pr/x+ps
=ps-qr/x^2