Page 6 - Mathematics Class - XII

CONTENTS

ACTIVITIES
UNIT - I : RELATIONS AND FUNCTIONS

TOPIC - 1: Relations and Functions

1.1 To verify that the relation R in the set A of all lines in a plane, defined by R = {(l, m): l ⊥ m} is 7
symmetric but neither reflexive nor transitive.

1.2 To verify that the relation R in the set A of all lines in a plane, defined by R = {(l, m): l || m} is 10
an equivalence relation.
1.3 To demonstrate a function that is not one-one but is onto. 13
1.4 To demonstrate a function which is one-one but not onto. 16

TOPIC - 2: Inverse Trigonometric Functions

2.1 To draw the graph of sin x, using the graph of sin x and demonstrate the concept of mirror 20
–1
reflection (about the line y = x).
2.2 To explore the principal value of the function sin x, using a unit circle. 24
–1

UNIT - III : CALCULUS

TOPIC - 3: Continuity and Differentiability

3.1 To sketch the graphs of a and log x, a > 0, a ≠ 1 and to examine that they are mirror images of 29
x
a
each other.
3.2 To establish a relationship between common logarithm (to the base 10) and natural logarithm 33
(to the base e) of the number x.
3.3 To find analytically the limit of a function f (x) at x = c and also check the continuity of the 37
function at that point.
3.4 To verify that for a function f to be continuous at given point x , Δ y = | f (x + Δ x) – f (x ) | is 40
0
0
0
arbitrarily small provided Δ x is sufficiently small.
3.5 To verify Rolle’s Theorem. 43
3.6 To verify Lagrange’s Mean Value Theorem. 47

TOPIC - 4: Application of Derivatives

4.1 To understand the concepts of decreasing and increasing functions. 51

4.2 To understand the concepts of local maxima, local minima and point of inflection. 54
4.3 To understand the concepts of absolute maximum and minimum values of a function in a given 57
closed interval through its graph.