Estimations with linear approximation ?Use linear approximations to estimate the following quantities. Choose a value of a to produce a small error. tan 3°

Solution 14E 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)(x a) STEP 2 Here,let f(x) = tan x ;and choose a=0 We get f () = sec x2 2 f(a) = tan 0 = 0and f (a = sec (0) = 1 Therefore the Linear approximation of the function,f(x),near a point x=a, is L(x) = f(a) + f a)(x a) = 0 + 1(x 0) = x L(x) = x STEP 3 According to the question tan 3 = tan( ) = f( ) {since 3 ( 60 60 ° degrees) means 60} f( ) L( ) 60 60 = 60= 0.0523 Therefore tan 3 0.0523