The THIRD-degree Maclaurin polynomial for $f(x)=e^x$ is used to approximate $f$ on $\left[0,2\right]$. What is the SMALLEST correct value of $M$ for $\left|f^{(4)}\right|$ on that interval, and what bound does it give?

The THIRD-degree Maclaurin polynomial for $f(x)=e^x$ is used to approximate $f$ on $\left[0,4\right]$. What is the SMALLEST correct value of $M$ for $\left|f^{(4)}\right|$ on that interval, and what bound does it give?

The SECOND-degree Maclaurin polynomial for a function $f$ is used to approximate $f\left(0.4\right)$. Taking $M=3$, what is the Lagrange error bound, rounded to four decimal places?

A student claims: "$\left|f^{(4)}\right|\le 4$ on $\left[4,4.5\right]$, so the error in the THIRD-degree Taylor approximation to $f\left(4.5\right)$ about $x=4$ is EXACTLY $\frac{4{\left(0.5\right)}^4}{24}$." Correct?

The FOURTH-degree Maclaurin polynomial for a function $f$ is used to approximate $f\left(0.5\right)$. Taking $M=3$, what is the Lagrange error bound, rounded to four decimal places?

The SECOND-degree Taylor polynomial for $f$ about $x=5$ is used to approximate $f\left(5.5\right)$, and $\left|f^{(3)}(x)\right|\le 7$ on that interval. Which expression BOUNDS the error?

What is the SMALLEST degree $n$ of a Maclaurin polynomial for $\sin x$ that guarantees an error less than $\frac{1}{10000}$ at $x=1$, taking $M=1$?

The THIRD-degree Taylor polynomial for $f$ about $x=4$ is used to approximate $f\left(4.8\right)$, and $\left|f^{(4)}(x)\right|\le 6$ on that interval. Which expression BOUNDS the error?

The SECOND-degree Maclaurin polynomial for $f(x)=e^x$ is used to approximate $f$ on $\left[0,3\right]$. What is the SMALLEST correct value of $M$ for $\left|f^{(3)}\right|$ on that interval, and what bound does it give?

The THIRD-degree Maclaurin polynomial for $f(x)=e^x$ is used to approximate $f$ on $\left[0,1\right]$. What is the SMALLEST correct value of $M$ for $\left|f^{(4)}\right|$ on that interval, and what bound does it give?

The FOURTH-degree Taylor polynomial for $f$ about $x=4$ is used to approximate $f\left(4.2\right)$, and $\left|f^{(5)}(x)\right|\le 5$ on that interval. Which expression BOUNDS the error?

The THIRD-degree Maclaurin polynomial for a function $f$ is used to approximate $f\left(0.5\right)$. Taking $M=2$, what is the Lagrange error bound, rounded to four decimal places?

The SECOND-degree Taylor polynomial for $f$ about $x=3$ is used to approximate $f\left(3.4\right)$, and $\left|f^{(3)}(x)\right|\le 9$ on that interval. Which expression BOUNDS the error?

The FOURTH-degree Maclaurin polynomial for a function $f$ is used to approximate $f\left(0.5\right)$. Taking $M=2$, what is the Lagrange error bound, rounded to four decimal places?

The THIRD-degree Maclaurin polynomial for a function $f$ is used to approximate $f\left(0.2\right)$. Taking $M=3$, what is the Lagrange error bound, rounded to four decimal places?

What is the SMALLEST degree $n$ of a Maclaurin polynomial for $\cos x$ that guarantees an error less than $\frac{1}{100000}$ at $x=1$, taking $M=1$?

The THIRD-degree Taylor polynomial for $f$ about $x=4$ is used to approximate $f\left(4.2\right)$, and $\left|f^{(4)}(x)\right|\le 3$ on that interval. Which expression BOUNDS the error?

A student claims: "$\left|f^{(4)}\right|\le 2$ on $\left[4,4.5\right]$, so the error in the THIRD-degree Taylor approximation to $f\left(4.5\right)$ about $x=4$ is EXACTLY $\frac{2{\left(0.5\right)}^4}{24}$." Correct?

What is the SMALLEST degree $n$ of a Maclaurin polynomial for $\sin x$ that guarantees an error less than $\frac{1}{200}$ at $x=1$, taking $M=1$?

The THIRD-degree Maclaurin polynomial for a function $f$ is used to approximate $f\left(0.4\right)$. Taking $M=3$, what is the Lagrange error bound, rounded to four decimal places?