Answer
$x_1\approx1.49870$
Work Step by Step
Step 1. Given $f(x)=x-1-0.5sin(x)$, we have $f'(x)=1-0.5cos(x)$.
Step 2. Use Newton’s method $x_{n+1}=x_n-\frac{f(x_n)}{f'(x_n)}$ to estimated the solution at $x_1$.
Step 3. Starting with $x_0=1.5$, we can get the result $x_1\approx1.49870$ as shown in the table.
