Linear and Quadratic Approximations In Exercises 8184, use a graphing utility to graph

Chapter 4, Problem 84

(choose chapter or problem)

Linear and Quadratic Approximations

In Exercises 81–84, use a graphing utility to graph the function. Then graph the linear and quadratic approximations

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

and

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

in the same viewing window. Compare the values of $f$, $P_{1}$ and $P_{2}$ and their first derivatives at x = a. How do the approximations change as you move farther away from x = a?

FUNCTION Value of a

$f(x)=\frac{\sqrt{x}}{x-1}$ a = 2

Equation Transcription:

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

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

$f$

${P}_{1}$

${P}_{2}$

$f(x)\ =\ \frac{\sqrt{\ x}}{x\ -\ 1}$

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

P_1

P_2

f(x) = sqrt x / x - 1

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.

Becoming a subscriber
Or look for another answer

Linear and Quadratic Approximations In Exercises 8184, use a graphing utility to graph

Login

Register

Linear and Quadratic Approximations In Exercises 8184, use a graphing utility to graph

Login

Register

Reset password