009A Sample Final A, Problem 8

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8. (a) Find the linear approximation to the function at the point .
    (b) Use to estimate the value of .

Recall that the linear approximation is the equation of the tangent line to a function at a given point. If we are given the point , then we will have the approximation . Note that such an approximation is usually only good "fairly close" to your original point .


Part (a):  
Note that . Since and , we have
Similarly, Together, this means that
Part (b):  
This is simply an exercise in plugging in values. We have


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