Answer the following questions, making it clear what steps you take to arrive at your answers. Round numerical parts of your answer to six (6) significant digits.

1. Using forward, backward, and central difference methods with step sizes t = 1; 0:5; 0:25, determine estimates for f (1), where f (t) = e t e t 2

2. Given the following data, estimate g (2:5) using a technique described in the "Discrete Function" section of the Differentiation chapter of the online textbook. x g(x) 0 1 1 4 2 7 3 6 4 3

3. Estimate R 2 0 e 2x sin(x) dx (a) using the Trapezoidal Rule with n = 1, 2, 4, and 8 segments, and (b) using Romberg Integration and the results of part (a)

4. Using 3-point and 4-point Gaussian Quadrature, determine approximations for Z 1 1 1:1x 3 + 7:5x 2 2:7 dx