2.3. Newton’s Forward Interpolation Formula

Try these first

1. 1.

   What is interpolation?

   Hint

   Think about why we need to predict values that aren't measured.

2. 2.

   State the formula for forward difference.

   Hint

   Consider how we calculate changes in values.

3. 3.

   What is the main use of Newton's Forward Interpolation?

   • Estimating unknown values
   • Calculating derivatives
   • Solving equations

   Hint

   Think about the context of numerical data.

4. 4.

   True or False: The formula is useful when the value of x is near the end of the dataset.

   • True
   • False

   Hint

   Reflect on the section's definition of applicability.

5. 5.

   Given the points (2, 3), (3, 5), (4, 7), apply Newton's Forward Interpolation to find f(2.5).

   Hint

   Ensure to calculate each difference and use the formula stepwise.

6. 6.

   Use data points f(1)=1, f(2)=8, f(3)=27 to estimate f(1.5).

   Hint

   Remember, you're working with differences between points!