Properties of Taylor Series

Consider the following statements about Taylor series.

I. The Taylor series for $e^x$ centered at $x=0$ is given by $1 + x + \frac{x^2}{2!} + \frac{x^3}{3!} + \cdots$.

II. The third-degree Taylor polynomial for $e^x$ provides an exact value for the function for all values of $x$.

III. The error in a Taylor polynomial approximation can be bounded using the remainder term from Taylor’s Theorem.

Which of the statements is/are true?