Linear approximation ?Write an equation of the line that represents the linear approximation To the following functions at a. Then (?a? ?graph the function and the linear approximation near a: (?? ?use the linear approximation to estimate the given quantity; and (?? ?compute the percent error in your approximation. f? ?) = tan? ?; ?a? =0; tan 1.5°

Solution 40E STEP 1 .The linear approximation formula is given by y = L(x) = f(a)+f (a)(xa) Given f(x) = tan x and a = 0. f(a) = tan 0 = 0 Then f (x) = sec x f(a) = sec 0 = 1 Therefore y = L(x) = 0+1(x0) = x Thus we get L(x) = x Thus we get the equation of the line as y = x STEP 2 (a).graph the function and the linear approximation near a: STEP 3 (b). use the linear approximation to estimate the given quantity; o We have to estimate the value of tan 1.5 using the linear approximation Thus we have o tan 1.5 L(1.5) = 1.5 o Thus tan 1.5 = 1.5 STEP 4 (c) .compute the percent error in your approximation. o The exact value of tan 1.5 = 0.026 |approxexact| |1.50.026| Therefore percent error = 100× |exact| = 100× |0.026|= 100×56.467 = 5646.7% percent error = 5646.7%