Solved: In Exercises 187190, (a) find the specified linear and quadratic approximations

Chapter 3, Problem 190

(choose chapter or problem)

Linear and Quadratic Approximations The linear and quadratic approximations of a function at x = a are \(P_{1}(x)=f^{\prime}(a)(x-a)+f(a)\) and \(P_{2}(x)=\frac{1}{2} f^{\prime \prime}(a)(x-a)^{2}+f^{\prime}(a)(x-a)+f(a)/).

In Exercises 187–190, (a) find the specified linear and quadratic approximations of f, (b) use a graphing utility to graph f and the approximations, (c) determine whether P1 or P2 is the better approximation, and (d) state how the accuracy changes as you move farther from x = a.

\(f(x)=\ln x ; \quad a=1\)

Text Transcription:

P_1(x)=f^prime(a)(x-a)+f(a)

P_2(x)=1/2 f^prime prime(a)(x-a)^2+f^prime(a)(x-a)+f(a)

f(x)=ln x; a=1