O que uma função faria se fosse aproximada por series de taylor?

To analyze whether a function $f(x)$ equals its Taylor series $T(x)$ centered at $x=a$ on an interval $(a-R,a+R)$, we can often use the Lagrange error bound to study the remainder $R_n(x) = f(x) - T_n(x)$ for each degree $n$ as $n\to\infty$. If $\lim_{n\to\infty} R_n(x) = 0$ for a given value of $x$, then $f(x) = T(x)$.