Linear and Quadratic Approximations In Exercises 5356, use a computer algebra system to

Chapter 3, Problem 55

(choose chapter or problem)

In Exercises 53–56, use a computer algebra system to find the linear approximation

$P_{1}(x)=f(a)+f^{\prime}(a)(x-a)$

and the quadratic approximation

$P_{2}(x)=f(a)+f^{\prime}(a)(x-a)+\frac{1}{2} f^{\prime \prime}(a)(x-a)^{2}$

to the function $f$ at x = a. Sketch the graph of the function and its linear and quadratic approximations.

f(x) = arctan x, a = 0

Equation Transcription:

${P}_{1}(x)=f(a)+f'(a)(x-a)$

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

$f$

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

Unfortunately, we don't have that question answered yet. But you can get it answered in just 5 hours by Logging in or Becoming a subscriber.

Login