Class 12: Maths Chapter 14 solutions. Complete Class 12 Maths Chapter 14 Notes.
RD Sharma Solutions for Class 12 Maths Chapter 14–Differentials, Errors and Approximations
RD Sharma 12th Maths Chapter 14, Class 12 Maths Chapter 14 solutions
Exercise 14.1 Page No: 14.9
1. If y = sin x and x changes from π/2 to 22/14, what is the approximate change in y?
Solution:
2. The radius of a sphere shrinks from 10 to 9.8 cm. Find approximately the decrease in its volume.
Solution:
Given the radius of a sphere changes from 10 cm to 9.8 cm.
Let x be the radius of the sphere and Δ x be the change in the value of x.
Hence, we have x = 10 and x + Δ x = 9.8
⇒ 10 + Δ x = 9.8
⇒ Δ x = 9.8 – 10
∴ Δ x = – 0.2
The volume of a sphere of radius x is given by
3. A circular metal plate expands under heating so that its radius increases by k%. Find the approximate increase in the area of the plate, if the radius of the plate before heating is 10 cm.
Solution:
4. Find the percentage error in calculating the surface area of a cubical box if an error of 1% is made in measuring the lengths of the edges of the cube.
Solution:
5. If there is an error of 0.1% in the measurement of the radius of a sphere, find approximately the percentage error in the calculation of the volume of the sphere.
Solution:
6. The pressure p and the volume v of a gas are connected by the relation pv1.4 = const. Find the percentage error in p corresponding to a decrease of ½ % in v.
Solution:
7. The height of a cone increases by k%, its semi-vertical angle remaining the same. What is the approximate percentage increase in (i) in total surface area, and (ii) in the volume, assuming that k is small.
Solution:
8. Show that the relative error in computing the volume of a sphere, due to an error in measuring the radius, is approximately equal to three times the relative error in the radius.
Solution:
RD Sharma Solutions for Class 12 Maths Chapter 14: Download PDF
RD Sharma Solutions for Class 12 Maths Chapter 14–Differentials, Errors and Approximations
Chapterwise RD Sharma Solutions for Class 12 Maths :
- Chapter 1–Relation
- Chapter 2–Functions
- Chapter 3–Binary Operations
- Chapter 4–Inverse Trigonometric Functions
- Chapter 5–Algebra of Matrices
- Chapter 6–Determinants
- Chapter 7–Adjoint and Inverse of a Matrix
- Chapter 8–Solution of Simultaneous Linear Equations
- Chapter 9–Continuity
- Chapter 10–Differentiability
- Chapter 11–Differentiation
- Chapter 12–Higher Order Derivatives
- Chapter 13–Derivatives as a Rate Measurer
- Chapter 14–Differentials, Errors and Approximations
- Chapter 15–Mean Value Theorems
- Chapter 16–Tangents and Normals
- Chapter 17–Increasing and Decreasing Functions
- Chapter 18–Maxima and Minima
- Chapter 19–Indefinite Integrals
About RD Sharma
RD Sharma isn't the kind of author you'd bump into at lit fests. But his bestselling books have helped many CBSE students lose their dread of maths. Sunday Times profiles the tutor turned internet star
He dreams of algorithms that would give most people nightmares. And, spends every waking hour thinking of ways to explain concepts like 'series solution of linear differential equations'. Meet Dr Ravi Dutt Sharma — mathematics teacher and author of 25 reference books — whose name evokes as much awe as the subject he teaches. And though students have used his thick tomes for the last 31 years to ace the dreaded maths exam, it's only recently that a spoof video turned the tutor into a YouTube star.
R D Sharma had a good laugh but said he shared little with his on-screen persona except for the love for maths. "I like to spend all my time thinking and writing about maths problems. I find it relaxing," he says. When he is not writing books explaining mathematical concepts for classes 6 to 12 and engineering students, Sharma is busy dispensing his duty as vice-principal and head of department of science and humanities at Delhi government's Guru Nanak Dev Institute of Technology.