Provide an appropriate response.
-Which of the following statements is false?
I. For a function $\mathrm { f } ( \mathrm { x } )$, the Taylor polynomial approximation can always be improved by increasing the degree of 1 polynomial.
II. Of all polynomials of degree less than or equal to $\mathrm { n }$, the Taylor polynomial of order $n$ gives the best approximi $f ( x )$.
III. The Taylor series at $x =$ a can be obtained by substituting $x - a$ for $x$ in the corresponding Maclaurin series.
A) I and II
B) I, II, and III
C) III only
D) I and III tion of

Question

Quizplus · Accepted Answer

The Answer of Provide an appropriate response.
-Which of the following statements is false?
I. For a function $\mathrm { f } ( \mathrm { x } )$, the Taylor polynomial approximation can always be improved by increasing the degree of 1 polynomial.
II. Of all polynomials of degree less than or equal to $\mathrm { n }$, the Taylor polynomial of order $n$ gives the best approximi $f ( x )$.
III. The Taylor series at $x =$ a can be obtained by substituting $x - a$ for $x$ in the corresponding Maclaurin series.
A) I and II
B) I, II, and III
C) III only
D) I and III tion of

Provide an Appropriate Response f(x)\mathrm { f } ( \mathrm { x } )f(x)

Provide an Appropriate Response $\mathrm { f } ( \mathrm { x } )$