Suppose you approximate $\sqrt{0.9}$ and $\sqrt{0.2}$ using the Taylor polynomial of degree 3 around x = 0 for the function $f(x)=\sqrt{1-x}$ .Which approximation is more accurate?
A)the approximation of $\sqrt{0.9}$
B)the approximation of $\sqrt{0.2}$

Question

Quizplus · Accepted Answer

The error in the Taylor approximation is $R_3(x) = \frac{f^{(4)}(c)}{4!} x^4$, where $c$ is some number between 0 and $x$. Since $f^{(4)}(x) = \frac{1}{8} (1-x)^{-5/2}$, the error is largest when $x$ is close to 1. Therefore, the approximation of $\sqrt{0.9}$ is more accurate than the approximation of $\sqrt{0.2}$.

Suppose You Approximate 0.9\sqrt{0.9}0.9​ And 0.2\sqrt{0.2}0.2​ Using the Taylor Polynomial of Degree 3 Around X =

Suppose You Approximate $\sqrt{0.9}$ And $\sqrt{0.2}$ Using the Taylor Polynomial of Degree 3 Around X =