Linear Approximations

# Linear Approximations - Linear Approximations In this...

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In this section we’re going to take a look at an application not of derivatives but of the tangent line to a function. Of course, to get the tangent line we do need to take derivatives, so in some way this is an application of derivatives as well. Given a function, , we can find its tangent at . The equation of the tangent line, which we’ll call for this discussion, is, Take a look at the following graph of a function and its tangent line. From this graph we can see that near the tangent line and the function have nearly the same graph. On occasion we will use the tangent line, , as an approximation to the function, , near . In these cases we call the tangent line the linear approximation to the function at . So, why would we do this? Let’s take a look at an example. Example 1 Determine the linear approximation for at . Use the linear approximation to approximate the value of

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Linear Approximations - Linear Approximations In this...

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