Question

find the Taylor polynomial T_3 for the following function at a = 1
f(x) = ln(x + 1)

Answer 1

What does \[T_3\] mean?

Answer 2

Third order Taylor polynomial.

Answer 3

Is that the third term in the series?

Answer 4

\[T_n(x) = \sum_{k = 0}^{n} \frac {f^{(k)} (a)}{k!} (x - a)^k\]Since you want a third order taylor polynomial, n is gonna be 3. So T_3 is the sum of all the terms up to k = 3.