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 :

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Q2 :  

Evaluate the Given limit:


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Q3 :  

Evaluate the Given limit:


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Q4 :  

Evaluate the Given limit:


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Q5 :  

Evaluate the Given limit:


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Q6 :  

Evaluate the Given limit:


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Q7 :  

Evaluate the Given limit:


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Q8 :  

Evaluate the Given limit:


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Q9 :  

Evaluate the Given limit:


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Q10 :  

Evaluate the Given limit:


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Q11 :  

Evaluate the Given limit:


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Q12 :  

Evaluate the Given limit:


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Q13 :  

Evaluate the Given limit:


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Q14 :  

Evaluate the Given limit:


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Q15 :  

Evaluate the Given limit:


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Q16 :  

Evaluate the given limit:

 


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Q17 :  

Evaluate the Given limit:

 


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Q18 :  

Evaluate the Given limit:

 


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Q19 :  

Evaluate the Given limit:

 


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Q20 :  

Evaluate the Given limit:

 


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Q21 :  

Evaluate the Given limit:

 


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Q22 :  


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Q23 :  

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


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Q24 :  

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


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Q25 :  

Evaluatef(x), where f(x) =


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Q26 :  

Findf(x), where f(x) =


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Q27 :  

Findf(x), where f(x) =


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Q28 :  

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


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Q29 :  

Letbe fixed real numbers and define a function

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


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Q30 :  

If f(x) =.

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


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Q31 :  

If the function f(x) satisfies, evaluate.


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Q32 :  

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


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<< 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.


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Q2 :  

Find the derivative of 99x at x = 100.


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Q3 :  

Find the derivative of x at x = 1.


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Q4 :  

Find the derivative of the following functions from first principle.

(i) x3 – 27 (ii) (x – 1) (x – 2)

(ii) (iv)


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Q5 :  

For the function

Prove that


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Q6 :  

Find the derivative offor some fixed real number a.


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Q7 :  

For some constants a and b, find the derivative of

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


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Q8 :  

Find the derivative offor some constant a.


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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)


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Q10 :  

Find the derivative of cos x from first principle.


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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


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<< 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)


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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)


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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):


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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


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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):


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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):


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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):


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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):


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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):


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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):


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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):


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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


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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


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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)


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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


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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):


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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):


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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):


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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


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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):


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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):


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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)


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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


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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)


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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):


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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):


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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):


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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):


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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)


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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):


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<< 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.

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