fx tanh x, a 0

Chapter 5, Problem 41

(choose chapter or problem)

Linear and Quadratic Approximations  In Exercises 41 and 42, use a computer algebra system to find the linear approximation

\(P_1(x)=f(a)+f'(a)(x-a)\)

and the quadratic approximation

\(P_2(x)=f(a)+f'(a)(x-a)+\frac{1}{2}f''(a)(x-a)^2\)

of the function f at x = a. Use a graphing utility to graph the function and its linear and quadratic approximations.

f(x) = tanh x,   a = 0

Text Transcription:

P_1 (x) = f(a) + f’(a)(x-a)

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

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