Sketch a curve of f(x)= sin(x)/x
Start by analysing the parts of the function, it's clearly a combination of two functions: f = g(x) / h(x) and drawing them both out.Examine behaviour for -inf. and +inf.Notice a problem in a situation when x = 0 as then the function would be infinity (key word "be" not tend)use appropriate methods to examine the point, use either the following: * L'Hospital rule *Use Taylor expansion or at least know and present understanding of the result * Use geometrical results and reciprocate them ie 1 < x/sin(x) < 1/cos(x) ergo cos(x) < sin(x)/x < 1 and as cos(0) = 1Despite the methods, we deduce in the end that the limx->0 sin(x)/x = 1 and the graph has an " o " at (0,1) to show it.
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