3 Review(s)

ACTIVITIES: 1: To verify that the relation R in the set L of all lines in a plane, defined by R = {(l,m): ^ m} is symmetric but neither reflexive nor transitive2: 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 relation3: To demonstrate a function which is not one-one but is onto4: To demonstrate a function which is one-one but not onto5: To draw the graph of sin–1 x, 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–1 x using a unit circle7: To sketch the graph of ax and loga x, a > 0, a # 1 and to examine that they are mirror images of each other8: To establish a relationship between common logarithm (to the base 10) and natural logarithm (to the base e) of the number x9: To find analytically the limit of a function f (x) at x = c and also to check the continuity of the function at that point10: To verify that for a function f to be continuous at given point x0, Dy = | f (x0 + Dx) – f (x0)| is arbitrarily small, provided Dx is sufficiently small11: To verify Rolle’s Theorem12: To verify Lagrange’s Mean Value Theorem13: To understand the concepts of decreasing and increasing functions14: To understand the concepts of local maxima, local minima and point of inflection15: To understand the concepts of absolute maximum and minimum values of a function in a given closed interval through its graph16: To construct an open box of maximum volume from a given rectangular sheet by cutting equal squares from each corner17: To find the time when the area of a rectangle of given dimensions become maximum, if the length is decreasing and the breadth increasing at given rates18: To verify that amongst all the rectangles of the same perimeter, the square has the maximum area19: To evaluate the definite integral òba Ö(1 – x2) dx as the limit of a sum and verify it by actual integration20: To verify geometrically that c × (a + b) = c × a + c × b21: To verify that angle in a semi-circle is a right angle, using vector method22: To locate the points to given coordinates in space, measure the distance between two points in space and then to verify the distance using distance formula23: To demonstrate the equation of a plane in normal form24: To verify that the angle between two planes is the same as the angle between their normal25: To find the distance of given point (in space) from a plane (passing through three non-collinear points) by actual measurement and also analytically26: To measure the shortest distance two skew-lines and verify it analytically27: 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 dicePROJECTS: 1: To minimize the cost of the food, meeting the dietary requirements of the staple food of the adolescent students of your school2: Estimation of the population of a particular region/country under the assumptions that there is no migration in or out of the existing population in a particular year3: Finding the coordinates of different points identified in your classroom using the concepts of three dimensional geometry and also find the distances between the identified points4: Formation of differential equation to explain the process of cooling of boiled water to a given room temperatureLog and Antilog