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Solved: Linear approximation Write an equation of the line
Chapter 4, Problem 42E(choose chapter or problem)
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; (b) use the linear approximation to estimate the given quantity, and (c) compute the percent error in your approximation.
\(f(x)=\cos x ; \quad a=\pi / 4 ; \cos (0.8)\)
Questions & Answers
QUESTION:
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; (b) use the linear approximation to estimate the given quantity, and (c) compute the percent error in your approximation.
\(f(x)=\cos x ; \quad a=\pi / 4 ; \cos (0.8)\)
ANSWER:Solution 42E STEP 1 .The linear approximation formula is given by y = L(x) = f(a)+f (a)(xa) Given f(x) = cos x and a = . 4 f(a) = cos( ) = 1 4 2 1 Then f (x) =sin x f(a) =sin 4 2 Therefore y = L(x) = 1(x )4= 1(1(x ) 4 2 2 2 1 Thus we get L(x) = 2(1x+ ) 4 Thus we get the e