Estimations with linear approximation ?Use linear approximations to estimate the following quantities. Choose a value of a to produce a small error. ln(1.05)

Solution 17E 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 Here,let f(x) = ln(x) ;and choose a=1 1 We get f (x) = x f(a) = ln 1 = 0 and f(a) = = 1 1 Therefore the Linear approximation of the function,f(x),near a point x=a, is L(x) = f(a)+f (a)(xa) L(x) = 0+1(x1) = x1 L(x) = x1 STEP 3 According to the question ln(1.05) = f(1.05) f(1.05) L(1.05) = 1.051 = 0.05 Therefore ln(1.05) 0.05