Solved: In Exercises 6972, use a computer algebra system to find the linear
Chapter 5, Problem 72(choose chapter or problem)
Linear and Quadratic Approximations In Exercises 69-72, use a computer algebra system to find the linear approximation \(P_{1}(x)=f(a)+f^{\prime}(a)(x-a)\) and the quadratic approximation \(P_{2}(x)=f(a)+f^{\prime}(a)(x-a)+\frac{1}{2} f^{\prime \prime}(a)(x-a)^{2}\) of the function f at x = a. Sketch the graph of the function and its linear and quadratic approximations.
f(x) = arctan x, a = 1
Text Transcription:
P_1( x) = f(a) + f^prime (a)(x-a)
P_{2}(x) = f(a)+f^prime (a) (x-a) + 1/2 f^prime prime (a) (x-a)^2
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