Mathematics: Use the Quadratic Approximation Error Bound to bound the error |f(x)−T2(x)| on the interval [-1,1]. True or false: The Quadratic Approximation Error Bound indicates that |f(x)−T2(x)|≤ 0.004307 for all x in I. True

C.c=(4x20)+8 is the correct one...

Use the Quadratic Approximation Error Bound to

paxbro3986

20.01.2022

$T(2)_{x} = 1 + \frac{1}{3} x + \frac{1}{18} x^{2}$

Step-by-step explanation:

Thinking process:

Let the function be: f(x)−T2(x)| on the interval [-1,1].

Then, if $f(x) =e^{\frac{x}{3} }$

Then $f(x)^{'1} = \frac{1}{3}e^{\frac{1}{3} }$

$f^{11}(x) = \frac{1}{9}e^{\frac{1}{3} } , then f^{11}/2 = 2!$

and so on..

Then the function becomes:

$T(2) x = 1 + \frac{1}{3}x + \frac{1}{18}x^{2}$

0,0(0 оценок)