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....
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.In this chapter, we have studied various types of functions and their graphs. The use of graphs also facilitate the study of..
Functions Limits and Continuity Conclusion
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.In this chapter, we have studied various types of functions and their graphs. The use of graphs also facilitate..
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..
Summary
If all the terms of the polynomial have a common factor, we take out the common factor and factorise. If the polynomial can be expressed as the difference of two squares, we use a 2 - b 2 = (a + b) (a - b)..
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