- ACTIVITIES
1. To verify that the relation R in the set L of all lines in a plane, defined by R = {(l, m) : l _ m}, is symmetric but neither reflexive nor transitive.
2. To verify that the relation R in the set L of all lines in a plane, defined by R = {(l, m) : l || m}, is an equivalence.
3. To demonstrate a function that is not one-to-one but is onto.
4. To demonstrate a function that is one-to-one but not onto.
5. To draw the graph of sin⁻¹x, using the graph of sin x and demonstrate the concept of mirror reflection (about the line y = x).
6. To explore the principal value of the function sin⁻¹x, using a unit circle.
7. To sketch the graphs of ax and logax, a > 0, a = 1, and to examine that they are mirror images of each other.
8. To establish a relationship between common logarithm (to the base 10) and natural logarithm (to the base e) of the number x.
9. To find analytically the limit of a function f(x) at x = c and also to check the continuity of the function at that point
10. To verify that for a function f to be continuous at a given point is arbitrarily small provided Ax is sufficiently small.
11. To understand the concepts of decreasing and increasing functions.
12. To understand the concept of local maxima, local minima, and point of inflection.
13. To understand the concepts of absolute maximum and minimum values of a function in a given closed interval through its graph.
14. To construct an open box of maximum volume from a given rectangular sheet by cutting equal squares from each corner.
15. To find the time when the area of a rectangle of given dimensions becomes maximum if the length is decreasing and the breadth is increasing at given rates.
16. To verify that amongst all the rectangles of the same perimeter, the square has the maximum area.
17. To verify that an angle in a semicircle is a right angle, use the vector method.
18. To locate the points at given coordinates in space, measure the distance between two points in space and then verify the distance using the distance formula.
19. To measure the shortest distance between two skew lines and verify it analytically.
20. To explain the computation of conditional probability of a given event A, when event B has already occurred, through an example of throwing a pair of dice.
