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Algebra of Limits
If f and g are two functions defined over same domain D, then we have certain set of identities which can be used for solving limits problems with variables like algebraic expression..
Expansions
In algebra we come across certain products very frequently. For e.g., (a + b) 2 , (a + b) 3 (a + b + c) 2 etc. These are nothing but products of binomials or trinomials. We derive the formulae for these products and apply them whenever necessary. These expansions help us to avoid elab..
Problems on Limits
Here is a list of problems solved using the identities of limits, standard limits, limits theorem explained above....
Framing of Formulae
Framing of Formulae - We use alphabets like x, y, z etc., to denote variables. For example the length of a rectangle is denoted by 'l'. It takes different values in different rectangles. A formula is a relation between different variables formed using mathematical symbols. Any g..
Framing of Formulae
We use alphabets like x, y, z etc., to denote variables. For example the length of a rectangle is denoted by 'l'. It takes different values in different rectangles. A formula is a relation between different variables formed using mathematical symbols. Any given condition can b..
Example 5:
Plot the graph of x+3y=6. Use the graph to find a) area between the line and axes b) value of y when x=..
Conclusion
In this chapter, we have studied various types of functions and their graphs. The use of graphs also facilitate the study of domain and range of functions...
Simultaneous inequations
Two inequalities, containing the same unknowns, are called equivalent, if they are valid at the same values of the unknowns. The same definition is used for the equivalence of two systems of simultaneous inequalities. Solving of inequalities is a process of transition from one inequ..
Examples:
(1) 2x 2 -1 = 0 (2) x 2 -5x+7 = 0 The solution to quadratic equations can be found using various techniques. One of them being, graph..
Example:
is satisfied for all the values of x. The sign is used to distinguish an identity from an equati..
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