Question

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Problem 1 Use the trapezoidal rule technique to approximate the following integrals: a) 「(x2+1)dr(Note: use 0.5 increments forx) b) sina d INote: use a MATLAB function to subdivide the interval into eight equal parts) c e dx (Note: use 0.25 increments for x Problem 2 Use the Simpson's rule to evaluate the following integrals aDdr Problem 3: Given the polynomial: x3-6x2 + 30-0, Use MATLAB to find all roots of this polynomial. Use MATLAB's polyval function to evaluate the above polynomial for the x values given: x[2 12 4 -31 a) b) Problem 4 Use MATLAB built in functions to come up with sequence of commands to graphically estimate where, and then calculate the 3 roots (solutions) of the following function: f(x) = e-15xsin(r) where -0.2 sxS 0.2 Problem S: An object is dropped straight down from a helicopter; the object falls faster and faster but its acceleration (rate of change of its velocity) decreases over time because of air resistance. The acceleration is measured in ft/sec2 and recorded every second after the drop for 5 sec, as shown: Time, t, (sec) 1 Acceleration, a 32.00 2 1.77 7.14 2.63 t/sec a) Use a MATLAB built in function to interpolate the acceleration at time 2.5 seconds, use linear b) Use a MATLAB built in function to interpolate the acceleration at time 2.5 seconds, use cubic c) What is the percentage error between the linear interpolation and the cubic spline interpolation interpolation spline interpolation in parts a and b above? Assume that the linear interpolation value is the "approximation", and the cubic spline interpolation value is the "actuar value. d) Use a MATLAB built in function to interpolate the time at which the acceleration is 5.45 ft/sec using linear interpolation. Problem 6 After the winter break, 3 students came to school sick with the flu. The following table shows the number of students infected with the flu depending on the number of days after the winter break. Time, (days) Number of infected 10 15 20 25 30 14 23 23 21 students What is the quadratic (2nd degree) model that best fit the data? What is the quartic (4" degree) model that best fit the data? Which model (quadratic or quartic) appears to better fit the data? Justify your choice. Using the better model, find the day at which the number of infected students will reach the maximum. Hint: First create NewTime from 0 to 30 days in increments of 0.5 day. Second, use polyval to evaluate the number of infected students for the NewTime using the coefficients of model that better fit the data. Third, find the location of maximum number of infections. Finally, find the NewTime value corresponding to the location of maximum number of infections) a) b) e) d) e) When will the number of infected students drop to zero? (Hint: The first time the model that better fit the data is Zero (first real root)

Answer 1

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