1.1 Convex Functions and Jenson’s Inequality A function is called a convex function if the line segment between any two points on the graph of the function lies above or on the graph. The following curve illustrates this oncept of a convex function and concave function: Fig 1.1 For a convex function , we… Continue reading
Tag: JEE Advanced
Week -8 | Inequalities – 1
1.1 Introduction We have already introduced the concept of inequations in our ‘Theory of Equations’ modules. To recollect: and with both this implies with this implies . We shall introduce ourselves to some advanced inequalities that are used in the modern world. 2.1 The AM-GM-HM Inequality Consider the positive real numbers . The following inequality is called… Continue reading
Week -7 | Sequences & Series – 8
Practice problems MCQ questions can have more than 1 correct answer. Q-1) If are in HP, then are in a) A.P b) G.P c) H.P d) None of these Q-2) Find the value of Q-3) The value of is a) b) c) d) None of these … Continue reading
Week -6 | Sequences & Series – 6
Q-1) Find the sum of , where . Solution: We have Q-2) Find the sum of Solution: We have the factors in the denominator in AP. In this case, what we normally do is to multiply and divide with the difference of the first factor and the last. Thus If we define , we have… Continue reading
Week -6 | Sequences & Series – 5
This is an optional module for the students preparing for engineering entrance examinations 1.1 Difference Equations By now that the difference between sequences and series is clear, we look at a new concept to solve recurrence relations related to sequences. Often we have our sequences defined by such a recurrence relation. For example, , with … Continue reading