Please show all of your work, including all the values of the function fff that you are using in part (b). You may present it as a grid, as shown in the PowerPoint slides.

How many data points (n) are needed for a 4th-order Newton polynomial interpolation? If xi =1,2,3,4,5,6,7 and the corresponding f(xi) values are given, which values of xi would you select to estimate f(3.2) using a 4th-order Newton polynomial interpolation? Specify the selected values as x1, x2, …, xn                                            (5 points)   2. The corresponding values of f(x) are provided at the following points:         x = 0,  1,   2,   3,   3.5,   4,   4.5,  5.0 Assuming that only Simpson’s rules may be used for numerical integration, explain how you would approach the evaluation of the integral over the given interval (0 to 5). Clearly indicate which Simpson’s rule(s) you would apply to each section and justify your choice. (5 points)

5. A function is represented as f(t) = 1  for 0 < t < 2    and        f(t) = 0  for 2 < t < 4 Compute the coefficients ao and bk by integration over an interval (0, 4). Show step by step integrations. Write the first three non-zero terms.

Choose the correct pronoun, considering the rules for pronoun agreement and reference.  The audience showed _____ appreciation with a standing ovation.

Dr. Branch tells his pregnant patient, “Because you are 38 years old, we are going to do amniocentesis to see whether your baby has a normal number of chromosomes.” What disorder is Dr. Branch most likely concerned about?

Candy is a 2-year-old with a moderate intellectual disability. She appears to have a single crease across the palm of her hand, slanted eyes, and a harsh voice. What diagnosis would Candy most likely be given?

Children and adolescents with PTSD experience recurrent, distressing memories of shocking experiences and traumas that include threat of, direct, or indirect experience with ____.

Describe the DSM-5 diagnostic criteria for autism spectrum disorder.

For both medication and cognitive-behavioral therapies, a critical factor for successful treatment of panic disorder is ____.

List and describe three different factors that moderate individuals’ stress responses.