NCERT Solutions for Class 12 Maths Chapter 6 Exercise 6.4 (Applications of Derivatives)
NCERT Solutions for Class 12 Maths Chapter 6 Exercise 6.4 contains all the questions with detailed solutions. Students are advised to solve these questions for better understanding of the concepts in exercise 6.4.
Krati Saraswat1 Feb, 2024
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NCERT Solutions for Class 12 Maths Chapter 6 Exercise 6.4 (Applications of Derivatives)
NCERT Solutions for Class 12 Maths Chapter 6 Exercise 6.4 Applications of Derivatives is prepared by the academic team of Physics Wallah. We have prepared NCERT Solutions for all exercise of Chapter 6. Given below is step by step solutions of all questions given in the NCERT Solutions for Class 12 Maths Chapter 6 Exercise 6.4.NCERT Solutions for Class 12 Maths Chapter 6 Exercise 6.4 Overview
NCERT Solutions for Class 12 Maths Chapter 6 Exercise 6.4 covers these important topics. Students are encouraged to review each topic thoroughly in order to fully understand the concepts taught in the chapter and make optimal use of the provided solutions. These solutions are the outcome of the dedicated effort that the Physics Wallah teachers have been doing to aid students in understanding the ideas covered in this chapter. After going over and rehearsing these responses, the goal is for students to easily score outstanding exam results.NCERT Solutions for Class 12 Maths Chapter 6 Exercise 6.4
Solve The Following Questions NCERT Solutions for Class 12 Maths Chapter 6 Exercise 6.4:NCERT Solutions for Class 12 Maths Chapter 6 Miscellaneous Exercise
Question 1. Using differentials, find the approximate value of each of the following up to 3 places of decimal:
(i) √25.3 (ii)√49.5 (iii)√0.6 (iv)(0.009) 1/3 (v)(0.999) 1/10 (vi) (15) 1/4 (vii) (26) 1/3 (viii) (255)1/4 (ix) (82) 1/4 (x) (401)1/2 (xi) (0.0037)1/2 (xii) (26.57) 1/3 (xiii) (81.5) 1/4 (xiv) (3.968) 3/2 (xv) (32.15) 1/5 Solution : (i) √25.3
(ii)
√49.5
(iii)
√0.6
(iv)
(0.009)
1/3
(v)
(0.999)
1/10
(vi)
(15)
1/4
(vii)
(26)
1/3
(viii)
(255)1/4
(ix)
(82)
1/4
(x)
(401)1/2
(xi)
(0.0037)1/2
(xii)
(26.57)
1/3
(xiii)
(81.5)
1/4
(xiv)
(3.968)
3/2
(xv) (32.15)
1/5
NCERT Solutions for Class 12 Maths Chapter 6 Exercise 6.1
Question 2. Find the approximate value off (2.01), where f(x) = 4x 2 + 5x + 2 Solution :
Hence, the approximate value of
f
(2.01) is 28.21.
NCERT Solutions for Class 12 Maths Chapter 6 Exercise 6.2
Question 3. Find the approximate value of f (5.001), wheref (x) =x 3 − 7x 2 + 15. Solution :
Hence, the approximate value of
f
(5.001) is −34.995.
NCERT Solutions for Class 12 Maths Chapter 6 Exercise 6.3
Question 4. Find the approximate change in the volume of a cube of side x meters caused by increasing the side by 1%. Solution :
Hence, the approximate change in the volume of the cube is 0.03
x
3
m
3
.
Question
5. Find the approximate change in the surface area of a cube of side x meters caused by decreasing the side by 1%.
Solution :
The surface area of a cube (
S)
of side
x
is given by
S
= 6
x
2
.
Hence, the approximate change in the surface area of the cube is 0.12
x
2
m
2
.
NCERT Solutions for Class 12 Maths Chapter 6 Exercise 6.5
Question 6. If the radius of a sphere is measured as 7 m with an error of 0.02 m, then find the approximate error in calculating its volume. Solution : Let r be the radius of the sphere and Δ r be the error in measuring the radius. Then, r = 7 m and Δ r = 0.02 m Now, the volume V of the sphere is given by,
Hence, the approximate error in calculating the volume is 3.92 π m
3
.
Question
7. If the radius of a sphere is measured as 9 m with an error of 0.03 m, then find the approximate error in calculating its surface area.
Solution :
Let
r
be the radius of the sphere and Δ
r
be the error in measuring the radius.
Then,
r
= 9 m and Δ
r
= 0.03 m
Now, the surface area of the sphere (
S)
is given by,
S
= 4πr
2
Hence, the approximate error in calculating the surface area is 2.16π m
2
.
Question
8. Iff (x) = 3x
2
+ 15x + 5, then the approximate value of f (3.02) is
A. 47.66
B. 57.66
C. 67.66
D.77.66
Solution :
Therefore, option (D) is correct.
Question
9. The approximate change in the volume of a cube of sidex metres caused by increasing the side by 3% is
A. 0.06x
3
m
3
B. 0.6x
3
m
3
C. 0.09x
3
m
3
D.0.9x
3
m
3
Solution :
The volume of a cube (
V
) of side
x
is given by
V
=
x
3
.
Therefore, option (C) is correct.
NCERT Solutions for Class 12 Maths Chapter 6 Exercise 6.4 FAQs
How many exercises are there in Chapter 6 Maths class 12?
Class 12 Maths Chapter 6 Application of Derivatives has 102 questions in 6 exercises along with 24 more provided in a miscellaneous exercise.
Why do we use derivatives?
The derivative can be used to find the equation of a tangent line to a graph at a particular point.
Why is class 12 so important?
If you want to get into a prestigious college, there is an eligibility criterion where your board marks matter. Hence, 12th board marks are crucial.
What is the basic concept of derivatives?
The derivative of a function describes the function's instantaneous rate of change at a certain point. Another common interpretation is that the derivative gives us the slope of the line tangent to the function's graph at that point.
What is the difference between derivative and differentiation?
The Derivative of a function in a point is a number; in general, is a function. The process of finding [computing] a derivative is called differentiation.
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