Part A: Find the local linear approximation of the function f(x)=3+x at x0=6, Part B use part A to approximate 8.9 as 9.1. Answers must be in fractions

Question

Part A: Find the local linear approximation of the function f(x)=3+x  at  x0=6,  Part B use part A to approximate 8.9  as  9.1. Answers must be in fractions

Aubree Mcintyre · Accepted Answer

Step 1: To Find  We have to find the local linear approximation of the function f(x)=3+x  at  x0=6  Also, approximate 8.9  as  9.1. Answers must be in fractions.  Step 2: Calculation  Solution (A): The linear approximation of  f(x) at x=a is L(x)≈f(a)+f(a)(x−a)  Now,  f(x)=3+x   f(x)=12{(3+x)}  Therefore, the linear approximation of f(x)=3+x  at  a=6 is  L(x)≈3+6+12{3+6}(x−6)    L(x)≈3+6+12{9}(x−6)    L(x)≈3+12×3(x−6)    L(x)≈3+16(x−6)    Solution (B): Since we get  f(5.9)=3+5.9=8.9≈3+16(5.9−6)=2.9833  f(5.9)=3+6.1=9.1≈3+16(6.1−6)=3.0166

Jeffrey Jordon · Accepted Answer

Answer is given below (on video)

Part A: Find the local linear approximation of the function f(x)=\sqrt{3+x}\t

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