Class 12 Maths Formulas Examples
Example 1: A circular disc of radius 7 cm is being heated. Due to expansion, its radius increases at a rate of 0.04 cm per second. Find the rate at which its area is increasing if the increased radius at any point is 8.4 cm.
Solution:
Let us assume that “r” be the radius of the given disc and “A” be the area, then the area is given as:
A = π x r2
Using the chain rule, and differentiation with respect to x,
dA/dt = 2 π r(dr/dt)
Thus, approximate rate of increase of radius = dr = (dr/dt) ∆t = 0.04 cm per second (given)
Hence, approximate rate of increase in area is,
dA = (dA/dt)(∆t)
dA = 2πr[(dr/dt) ∆t]
= 2π (8.4) (0.04)
= 0.672π cm2 per second.
Therefore, when r = 8.4 cm, then the area is increasing at a rate of 0.672π cm2 per second.
Example 2: Find the distance between the points, (2, 3) and (11, 1)
Solution:
Given points, (2, 3) and (11, 1) then using the distance formula the distance between the points is,
d = √{(11 – 2)2 + (1 – 3)2} = √{92 + (-2)2}
d = √(81 + 4) = √(85)
Thus, the distance between th points, (2, 3) and (11, 1) is √(85) units.
Example 3: Find the magnitude of the Vector A = 3i + 4j + 5k.
Solution:
Given vectior A = 3i + 4j + 5k
Magnitude ofn Vect A = |A|
using magnitude of vector formula,
|A| = √(32 + 42 + 52) = √(9 + 16 + 25)
|A| = √(50) = 5√(2)
Thus, the magnitude of the vector A = 3i + 4j + 5k is 5√(2).
Class 12 Maths Formulas
Class 12 maths formulas page is designed for the convenience of the learners so that one can understand all the important concepts of Class 12 Mathematics directly and easily. Math formulae for Class 12 are for the students who find mathematics to be a nightmare and difficult to grasp. They may become hesitant and lose interest in studies as a result of this. We have included all of the key formulae for the 12th standard Maths topic, which students may simply recall, to assist them in understanding Maths in a straightforward manner. For all courses such as Integration, Differentiation, Trignometry, Relation and Functions, and so on, the formulae are provided here according to the NCERT curriculum.
Table of Content
- Chapter 1: Relations and Functions
- Chapter 2: Inverse Trigonometric Functions
- Chapter 3: Matrices
- Chapter 4: Determinants
- Chapter 5: Continuity and Differentiability
- Chapter 6: Applications of Derivatives
- Chapter 7: Integrals
- Chapter 8: Applications of Integrals
- Chapter 9: Differential Equations
- Chapter 10: Vector Algebra
- Chapter 11: Three-Dimensional Geometry
- Chapter 12: Linear Programming
- Chapter 13: Probability
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