NCERT Solutions for Class 11 Maths Maths Chapter 13

Limits and Derivatives Class 11

Chapter 13 Limits and Derivatives Exercise 13.1, 13.2, miscellaneous Solutions

<< Previous Chapter 12 : Introduction to Three Dimensional Geometry Next Chapter 14 : Mathematical Reasoning >>

Exercise 13.1 : Solutions of Questions on Page Number : 301

Q1 :  

Evaluate the Given limit:


Answer :

Answer needs Correction? Click Here

Q2 :  

Evaluate the Given limit:


Answer :

Answer needs Correction? Click Here

Q3 :  

Evaluate the Given limit:


Answer :

Please Register/Login to get access to all solutions Facebook Login
Q4 :  

Evaluate the Given limit:


Answer :

Please Register/Login to get access to all solutions Facebook Login
Q5 :  

Evaluate the Given limit:


Answer :

Please Register/Login to get access to all solutions Facebook Login
Q6 :  

Evaluate the Given limit:


Answer :

Please Register/Login to get access to all solutions Facebook Login
Q7 :  

Evaluate the Given limit:


Answer :

Please Register/Login to get access to all solutions Facebook Login
Q8 :  

Evaluate the Given limit:


Answer :

Please Register/Login to get access to all solutions Facebook Login
Q9 :  

Evaluate the Given limit:


Answer :

Please Register/Login to get access to all solutions Facebook Login
Q10 :  

Evaluate the Given limit:


Answer :

Please Register/Login to get access to all solutions Facebook Login
Q11 :  

Evaluate the Given limit:


Answer :

Please Register/Login to get access to all solutions Facebook Login
Q12 :  

Evaluate the Given limit:


Answer :

Please Register/Login to get access to all solutions Facebook Login
Q13 :  

Evaluate the Given limit:


Answer :

Please Register/Login to get access to all solutions Facebook Login
Q14 :  

Evaluate the Given limit:


Answer :

Please Register/Login to get access to all solutions Facebook Login
Q15 :  

Evaluate the Given limit:


Answer :

Please Register/Login to get access to all solutions Facebook Login
Q16 :  

Evaluate the given limit:

 


Answer :

Please Register/Login to get access to all solutions Facebook Login
Q17 :  

Evaluate the Given limit:

 


Answer :

Please Register/Login to get access to all solutions Facebook Login
Q18 :  

Evaluate the Given limit:

 


Answer :

Please Register/Login to get access to all solutions Facebook Login
Q19 :  

Evaluate the Given limit:

 


Answer :

Please Register/Login to get access to all solutions Facebook Login
Q20 :  

Evaluate the Given limit:

 


Answer :

Please Register/Login to get access to all solutions Facebook Login
Q21 :  

Evaluate the Given limit:

 


Answer :

Please Register/Login to get access to all solutions Facebook Login
Q22 :  


Answer :

Please Register/Login to get access to all solutions Facebook Login
Q23 :  

Find f(x) andf(x), where f(x) =


Answer :

Please Register/Login to get access to all solutions Facebook Login
Q24 :  

Find f(x), where f(x) =


Answer :

Please Register/Login to get access to all solutions Facebook Login
Q25 :  

Evaluatef(x), where f(x) =


Answer :

Please Register/Login to get access to all solutions Facebook Login
Q26 :  

Findf(x), where f(x) =


Answer :

Please Register/Login to get access to all solutions Facebook Login
Q27 :  

Findf(x), where f(x) =


Answer :

Please Register/Login to get access to all solutions Facebook Login
Q28 :  

Suppose f(x) = and iff(x) = f(1) what are possible values of a and b?


Answer :

Please Register/Login to get access to all solutions Facebook Login
Q29 :  

Letbe fixed real numbers and define a function

What isf(x)? For some computef(x).


Answer :

Please Register/Login to get access to all solutions Facebook Login
Q30 :  

If f(x) =.

For what value (s) of a does f(x) exists?


Answer :

Please Register/Login to get access to all solutions Facebook Login
Q31 :  

If the function f(x) satisfies, evaluate.


Answer :

Please Register/Login to get access to all solutions Facebook Login
Q32 :  

If. For what integers m and n does and exist?


Answer :

Please Register/Login to get access to all solutions Facebook Login
<< Previous Chapter 12 : Introduction to Three Dimensional Geometry Next Chapter 14 : Mathematical Reasoning >>

Exercise 13.2 : Solutions of Questions on Page Number : 312

Q1 :  

Find the derivative of x2 - 2 at x = 10.


Answer :

Please Register/Login to get access to all solutions Facebook Login
Q2 :  

Find the derivative of 99x at x = 100.


Answer :

Please Register/Login to get access to all solutions Facebook Login
Q3 :  

Find the derivative of x at x = 1.


Answer :

Please Register/Login to get access to all solutions Facebook Login
Q4 :  

Find the derivative of the following functions from first principle.

(i) x3 – 27 (ii) (x – 1) (x – 2)

(ii) (iv)


Answer :

Please Register/Login to get access to all solutions Facebook Login
Q5 :  

For the function

Prove that


Answer :

Please Register/Login to get access to all solutions Facebook Login
Q6 :  

Find the derivative offor some fixed real number a.


Answer :

Please Register/Login to get access to all solutions Facebook Login
Q7 :  

For some constants a and b, find the derivative of

(i) (x – a) (x – b) (ii) (ax2 + b)2 (iii)


Answer :

Please Register/Login to get access to all solutions Facebook Login
Q8 :  

Find the derivative offor some constant a.


Answer :

Please Register/Login to get access to all solutions Facebook Login
Q9 :  

Find the derivative of

(i) (ii) (5x3 + 3x – 1) (x – 1)

(iii) x–3 (5 + 3x) (iv) x5 (3 – 6x–9)

(v) x–4 (3 – 4x–5) (vi)


Answer :

Please Register/Login to get access to all solutions Facebook Login
Q10 :  

Find the derivative of cos x from first principle.


Answer :

Please Register/Login to get access to all solutions Facebook Login
Q11 :  

Find the derivative of the following functions:

(i) sin x cos x (ii) sec x (iii) 5 sec x + 4 cos x

(iv) cosec x (v) 3cot x + 5cosec x

(vi) 5sin x - 6cos x + 7 (vii) 2tan x - 7sec x


Answer :

Please Register/Login to get access to all solutions Facebook Login
<< Previous Chapter 12 : Introduction to Three Dimensional Geometry Next Chapter 14 : Mathematical Reasoning >>

Exercise Miscellaneous : Solutions of Questions on Page Number : 317

Q1 :  

Find the derivative of the following functions from first principle:

(i) –x (ii) (–x)–1 (iii) sin (x + 1)

(iv)


Answer :

Please Register/Login to get access to all solutions Facebook Login
Q2 :  

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): (x + a)


Answer :

Please Register/Login to get access to all solutions Facebook Login
Q3 :  

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):


Answer :

Please Register/Login to get access to all solutions Facebook Login
Q4 :  

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): (ax + b) (cx + d)2


Answer :

Please Register/Login to get access to all solutions Facebook Login
Q5 :  

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):


Answer :

Please Register/Login to get access to all solutions Facebook Login
Q6 :  

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):


Answer :

Please Register/Login to get access to all solutions Facebook Login
Q7 :  

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):


Answer :

Please Register/Login to get access to all solutions Facebook Login
Q8 :  

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):


Answer :

Please Register/Login to get access to all solutions Facebook Login
Q9 :  

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):


Answer :

Please Register/Login to get access to all solutions Facebook Login
Q10 :  

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):


Answer :

Please Register/Login to get access to all solutions Facebook Login
Q11 :  

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):


Answer :

Please Register/Login to get access to all solutions Facebook Login
Q12 :  

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): (ax + b)n


Answer :

Please Register/Login to get access to all solutions Facebook Login
Q13 :  

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): (ax + b)n (cx + d)m


Answer :

Please Register/Login to get access to all solutions Facebook Login
Q14 :  

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): sin (x + a)


Answer :

Please Register/Login to get access to all solutions Facebook Login
Q15 :  

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): cosec x cot x


Answer :

Please Register/Login to get access to all solutions Facebook Login
Q16 :  

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):


Answer :

Please Register/Login to get access to all solutions Facebook Login
Q17 :  

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):


Answer :

Please Register/Login to get access to all solutions Facebook Login
Q18 :  

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):


Answer :

Please Register/Login to get access to all solutions Facebook Login
Q19 :  

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): sinn x


Answer :

Please Register/Login to get access to all solutions Facebook Login
Q20 :  

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):


Answer :

Please Register/Login to get access to all solutions Facebook Login
Q21 :  

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):


Answer :

Please Register/Login to get access to all solutions Facebook Login
Q22 :  

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): x4 (5 sin x - 3 cos x)


Answer :

Please Register/Login to get access to all solutions Facebook Login
Q23 :  

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): (x2 + 1) cos x


Answer :

Please Register/Login to get access to all solutions Facebook Login
Q24 :  

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): (ax2 + sin x) (p + q cos x)


Answer :

Please Register/Login to get access to all solutions Facebook Login
Q25 :  

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):


Answer :

Please Register/Login to get access to all solutions Facebook Login
Q26 :  

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):


Answer :

Please Register/Login to get access to all solutions Facebook Login
Q27 :  

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):


Answer :

Please Register/Login to get access to all solutions Facebook Login
Q28 :  

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):


Answer :

Please Register/Login to get access to all solutions Facebook Login
Q29 :  

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): (x + sec x) (x - tan x)


Answer :

Please Register/Login to get access to all solutions Facebook Login
Q30 :  

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):


Answer :

Please Register/Login to get access to all solutions Facebook Login
<< Previous Chapter 12 : Introduction to Three Dimensional Geometry Next Chapter 14 : Mathematical Reasoning >>

Maths - Maths : CBSE NCERT Exercise Solutions for Class 11th for Limits and Derivatives ( Exercise 13.1, 13.2, miscellaneous ) will be available online in PDF book form soon. The solutions are absolutely Free. Soon you will be able to download the solutions.

Popular Articles
Exercise 13.1
Question 1
Question 2
Question 3
Question 4
Question 5
Question 6
Question 7
Question 8
Question 9
Question 10
Question 11
Question 12
Question 13
Question 14
Question 15
Question 16
Question 17
Question 18
Question 19
Question 20
Question 21
Question 22
Question 23
Question 24
Question 25
Question 26
Question 27
Question 28
Question 29
Question 30
Question 31
Question 32
Exercise 13.2
Question 1
Question 2
Question 3
Question 4
Question 5
Question 6
Question 7
Question 8
Question 9
Question 10
Question 11
Exercise Miscellaneous
Question 1
Question 2
Question 3
Question 4
Question 5
Question 6
Question 7
Question 8
Question 9
Question 10
Question 11
Question 12
Question 13
Question 14
Question 15
Question 16
Question 17
Question 18
Question 19
Question 20
Question 21
Question 22
Question 23
Question 24
Question 25
Question 26
Question 27
Question 28
Question 29
Question 30