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Lecture_3_9 - " x If" x is small then the tangent...

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Section 3.9 Differentials and Linear Approximations Page 245: 5, 7, 9,15,17 Idea: Using the tangent line for approximations to the curve near a particular point. The tangent line can be called the linearization of the curve at a point (a, f(a)). L ( x ) = f ( a ) + " f ( a )( x # a ) dy dx denotes the slope of the curve at point; or the slope of the tangent line dy is “the differential” ; it is the change in the y-values along the tangent line when you go dx = " x along the independent axis. dy dx = " f ( x ) dy = " f ( x ) # dx " y is the actual change in the function when you go
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Unformatted text preview: " x . If " x is small then the tangent line is a good approximation to the function or the differential is a good approximation to the true change in y values dy " # y Example: 1. Find the equation of the tangent line to f ( x ) = tan x at x = 0. Use the tangent line to approximate the value of tan(.25) . (use your calculator to see how close this approximation is to the true value) 2. ( #15 in text h/w) Use a linear approximation (or differentials) to estimate the given number (2.001) 5...
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