Answer
$3.141592654$
Work Step by Step
Step 1. Given $f(x)=tan(x)$, we have $f'(x)=sec^2(x)$.
Step 2. Using Newton’s method $x_{n+1}=x_n-\frac{f(x_n)}{f'(x_n)}$ with a starting point $x_0=3$, we can obtain the estimation of $\pi$ as shown in the table as $3.141592654$
