Use linear approximations to estimate the following quantities. Choose a value of a to produce a small error.

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Solution 13E STEP 1 Linear approximation is a method of estimating the value of a function,f(x),near a point x=a,using the formula L(x) = f(a)+f (a)(xa) STEP 2 1 Here,let f(x) = x ;and choose a=200 We get f (x) = x2 f(a) = 200 = 0.005and f (a) = 12 =0.000025 200 Therefore the Linear approximation of the function,f(x),near a point x=a, is L(x) = f(a)+f (a)(xa) = 0.0050.000025(x200) = 0.0050.000025x+0.005 = 0.010.000025x L(x) = 0.010.000025x STEP 3 According to the question 1 = 1 = f(203) x 203 f(203) L(203) = 0.010.000025×203 = 0.004925 Therefore 1 0.004925 203