Graph/Limit of sin(x)/x, Graph of tangent of sin(x)
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1) The limit of f(x) = (sin x)/x as x approaches 0 is 1.
a) Use a graphing utility to graph the function f on the interval (- pi (<=) 0 (<=) pi )
(meaning negative pi is less than or equal to zero which is less than or equal to pi)
Explain how the graph helps confirm the theorem.
b) Explain how you could use a table of values to confirm the value of this limit numerically.
c) Graph g(x) = sin x by hand. Sketch a tangent line at the point (0,0) and visually estimate the slope of this tangent line.
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Solution Summary
The attached solution takes a look at the limit of the function sin(x)/x as x approaches 1. Excel is used to graph the function from -pi to pi. The excel sheet is given to show how one would create the graph. The graph of g(x)=sin x is also considered with a tangent line drawn at 0,0.
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