009A Sample Final A, Problem 8
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Revision as of 10:09, 24 March 2015 by MathAdmin (Created page with "<br> <span style="font-size:135%"> <font face=Times Roman>8. (a) Find the linear approximation <math style="vertical-align: -14%;">L(x)</math> to the function <math style="ver...")
8. (a) Find the linear approximation to the function at the point .
(b) Use to estimate the value of .
|Recall that the linear approximation L(x) is the equation of the tangent line to a function at a given point. If we are given the point x0, then we will have the approximation . Note that such an approximation is usually only good "fairly close" to your original point x0.|
|Note that f '(x) = sec x tan x. Since sin (π/3) = √3/2 and cos (π/3) = 1/2, we have|
|Similarly, f(π/3) = sec (π/3) = 2. Together, this means that|
|This is simply an exercise in plugging in values. We have|