1. **Problem Statement:** Find the value of $y$ at $x=1.75$ using Gauss's forward interpolation formula given the data points: | $x$ | 1.72 | 1.73 | 1.74 | 1.75 | 1.76 | 1.77 | |-----|------|------|------|------|------|------| | $y$ | ? | ? | ? | ? | ? | ? | (Note: Since the user did not provide $y$ values, we assume the problem is to explain the method.) 2. **Formula:** Gauss's forward interpolation formula is: $$ P(x) = y_0 + p\Delta y_0 + \frac{p(p-1)}{2!}\Delta^2 y_0 + \frac{p(p-1)(p-2)}{3!}\Delta^3 y_0 + \cdots $$ where $p = \frac{x - x_0}{h}$, $h$ is the equal spacing between $x$ values, $y_0$ is the first value, and $\Delta$ denotes forward differences. 3. **Steps:** - Calculate $h = 1.73 - 1.72 = 0.01$. - Calculate $p = \frac{1.75 - 1.72}{0.01} = 3$. - Construct the forward difference table for $y$ values. - Apply the formula using the differences and $p$. 4. **Explanation:** Gauss's forward formula uses the value at the starting point and adds corrections based on the forward differences weighted by $p$ terms. 5. **Final answer:** Cannot compute exact $y$ without given $y$ values. Please provide $y$ values for complete solution.