If f(x) is an nth-degree polynomial and $P_{n} (x)$ is the nth Taylor polynomial for f at $x_{0}$ , what is the nth remainder $R_{n} (x)$ ? What is $R_{n + 1} (x)$ ?

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If f(x) is an nth-degree polynomial and $P_{n} (x)$ is the nth Taylor polynomial for f at $x_{0}$ , what is the nth remainder $R_{n} (x)$ ? What is $R_{n + 1} (x)$ ?

Accepted Answer

Thus, the required remainders are $R_{n} (x) = \frac{f^{n + 1} (c)}{(n + 1)!} {(x - x_{0})}^{n + 1} a n d R_{n + 1} (x) = \frac{f^{n + 2} (c)}{(n + 2)!} {(x - x_{0})}^{n + 2}$

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If f(x) is an nth-degree polynomial and $P_{n} (x)$ is the nth Taylor polynomial for f at $x_{0}$ , what is the nth remainder $R_{n} (x)$ ? What is $R_{n + 1} (x)$ ?

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If f(x) is an nth-degree polynomial and Pn(x) is the nth Taylor polynomial for f at x0, what is the nth remainder Rn(x)? What is Rn+1(x)?

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If f(x) is an nth-degree polynomial and $P_{n} (x)$ is the nth Taylor polynomial for f at $x_{0}$ , what is the nth remainder $R_{n} (x)$ ? What is $R_{n + 1} (x)$ ?