In This Post we are providing Chapter -12 |Limits and Derivatives |NCERT Solutions for Class 11 Maths which will be beneficial for students. These solutions are updated according to 2021-22 syllabus. These Class 11 can be really helpful in the preparation of Limits and Derivatives Board exams and will provide you with in depth detail of the chapter.
We have solved every question stepwise so you don’t have to face difficulty in understanding the solutions. It will also give you concepts that are important for overall development of students. Class 11 Maths Limits and Derivatives NCERT Written Solutions will be useful in higher classes as well because variety of questions related to these concepts can be asked so you must study and understand them properly.
Table of Contents
Class 11th Chapter -13 LIMITS AND DERIVATIVES | NCERT MATHS SOLUTION |
Evaluate the following limits in Exercises 1 to 22.
Ex 13.1 Class 11 Maths Question 1.
Solution:
Ex 13.1 Class 11 Maths Question 2.
Solution:
Ex 13.1 Class 11 Maths Question 3.
Solution:
Ex 13.1 Class 11 Maths Question 4.
Solution:
Ex 13.1 Class 11 Maths Question 5.
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Ex 13.1 Class 11 Maths Question 6.
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Ex 13.1 Class 11 Maths Question 7.
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Ex 13.1 Class 11 Maths Question 8.
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Ex 13.1 Class 11 Maths Question 9.
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Ex 13.1 Class 11 Maths Question 10.
Solution:
Ex 13.1 Class 11 Maths Question 11.
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Ex 13.1 Class 11 Maths Question 12.
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Ex 13.1 Class 11 Maths Question 13.
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Ex 13.1 Class 11 Maths Question 14.
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Ex 13.1 Class 11 Maths Question 15.
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Ex 13.1 Class 11 Maths Question 16.
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Ex 13.1 Class 11 Maths Question 17.
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Ex 13.1 Class 11 Maths Question 18.
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Ex 13.1 Class 11 Maths Question 19.
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Ex 13.1 Class 11 Maths Question 20.
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Ex 13.1 Class 11 Maths Question 21.
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Ex 13.1 Class 11 Maths Question 22.
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Ex 13.1 Class 11 Maths Question 23.
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Ex 13.1 Class 11 Maths Question 24.
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Ex 13.1 Class 11 Maths Question 25.
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Ex 13.1 Class 11 Maths Question 26.
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Ex 13.1 Class 11 Maths Question 27.
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Ex 13.1 Class 11 Maths Question 28.
Solution:
Adding (ii) and (iii), we get 2b = 8 ⇒ b = 4
Subtituting the value of b in (iii), we get
4 – a = 4 ⇒ a = 0
Thus a = 0 and b = 4.
Ex 13.1 Class 11 Maths Question 29.
Solution:
Ex 13.1 Class 11 Maths Question 30.
Solution:
Ex 13.1 Class 11 Maths Question 31.
Solution:
Ex 13.1 Class 11 Maths Question 32.
Solution:
We hope the NCERT Solutions for Class 11 Maths Chapter 13 Limits and Derivatives Ex 13.1 help you. If you have any query regarding NCERT Solutions for Class 11 Maths Chapter 13 Limits and Derivatives Ex 13.1, drop a comment below and we will get back to you at the earliest.
Ex 13.2 Class 11 Maths Question 1.
Find the derivative of x2 – 2 at x = 10.
Solution:
let f(x) = x2 – 2
Differentiating (i) with respect to x, we get
f'(x) = 2x
At x = 10, f'(10) = 2(10) = 20.
Ex 13.2 Class 11 Maths Question 2.
Find the derivative of 99x at x = 10.
Solution:
let f(x) = 99x
Differentiating (i) with respect to x, we get
f'(x) = 90
At x = 100, f'(100) = 99.
Ex 13.2 Class 11 Maths Question 3.
Find the derivative of x at x = 10.
Solution:
let f(x) = x
Differentiating (i) with respect to x, we get
f'(x) = 1
At x = 1, f'(1) = 1.
Ex 13.2 Class 11 Maths Question 4.
Find the derivative of the following functions from first principle.
(i) x3 – 27
(ii) (x – 1)(x – 2)
(iii)
(iv)
Solution:
Ex 13.2 Class 11 Maths Question 5.
For the function
Prove that f'(1) = 100f'(0)
Solution:
We have
Ex 13.2 Class 11 Maths Question 6.
Find the derivative of xn + axn-1 + a2xn-2+
…. + an-1x + an for some fixed real number a.
Solution:
Let f(x) = xn + axn-1 + a2xn-2+
…. + an-1x + an
Differentiating (i) with respect to x, we get
f'(x) = nxn-1 + (n – 1)axn-2 + …… + an-1
Ex 13.2 Class 11 Maths Question 7.
For some constants a and b, find the derivative of
(i) (x – a)(x – b)
(ii) (ax2 + b)2
(iii)
Solution:
(i) Let f(x) = (x – a)(x – b) ….(1)
Differentiating (1) with respect to x, we get
f'(x) = (x – a)(x – b)’ + (x – a)’ (x – b)
⇒ f'(x) = (x – a) + (x – b) = 2x – a – b
Ex 13.2 Class 11 Maths Question 8.
Find the derivative 
Solution:
Let f(x) =
Differentiating (i) with respect to x, we get
Ex 13.2 Class 11 Maths Question 9.
Find the derivative of
Solution:
(i) Let f(x) = 
Differentiating (i) with respect to x, we get
f'(x) = 2·1 – 0 ⇒ f'(x) = 2.
(ii) Let f(x) = 5x3 + 3x – 1)(x – 1)
Ex 13.2 Class 11 Maths Question 10.
Find the derivative of cos x from first principle.
Solution:
Let f(x) = cos x
Ex 13.2 Class 11 Maths Question 11.
Find the derivative of the following functions:
(i) sin x cos x
(ii) secx
(iii) 5 secx + 4 cosx
(iv) cosecx
(v) 3 cotx + 5 cosecx
(vi) 5sinx – 6 cosx + 7
(vii) 2 tanx – 7 secx.
Solution:
(i) Let f(x) = sin x cos x … (1)
Differentiating (1) with respect to x, we get
We hope the NCERT Solutions for Class 11 Maths Chapter 13 Limits and Derivatives Ex 13.2 help you. If you have any query regarding NCERT Solutions for Class 11 Maths Chapter 13 Limits and Derivatives Ex 13.2, drop a comment below and we will get back to you at the earliest.
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