QUESTION 12 IN MATLAB

olving Equations 4. Carry out the steps of Computer Problem! 3 for (a) f(x) = 2e-1-x2-1 5. A silo composed of a right circular cylinder of height 10 m surmounted by a hemispherical 6. A 10-cm-high cone contains 60 cm2 of ice cream, including a hemispherical scoop on top. Find 7. Consider the function f(x) = esin, + x6-2x4-3-1 on the interval [-2.2. Plot the (b) f(x) In(3-x) + x-2. dome contains 400 m3 of volume. Find the base radius of the silo to four places. 1.5 ROOT-FINDING correct decimal the radius of the scoop to four correct decimal places. function on the interval, and find all three roots to six correct decimal places. Determine which roots converge quadratically, and find the multiplicity of the roots that converge linearly Carry out the steps of Computer Problem 7 for the function f(x) = 94cos3x-24cos x + 177 sin2x-108 sin4r-72cos, sinh-65 on the interval 8. 9. Apply Newton's Method to find both roots of the function f(x) = 14xe-2-12-2- 7+20x2-26x + 12 on the interval [(0,3]. For each root, print out the sequence of tierates, the errors ei, and the relevant error ratio ei +1 or ei +1 /ei that converges to a nonzero limit. Match the limit with the expected value M from Theorem 1.11 or S from Theorem 1.12. Set ,f(x) = 54x6 + 45x5-102x4-69x3 + 35x2 + 16x-4. Plot the function on the interval [-2,2], and use Newton's Method to find all five roots in the interval. Determine for which roots Newton converges linearly and for which the convergence is quadratic. 10. The ideal gas law for a gas at low temperature and pressure is PV = nRT, where P is pressure (in atm), V is volume (in L), T is temperature (in K), n is the number of moles of the gas, and R 0.0820578 is the molar gas constant. The van der Waals equation 11. V2 covers the nonideal case where these assumptions do not hold. Use the ideal gas law to compute an initial guess, followed by Newton's Method applied to the van der Waals equation to find the volume of one mole of oxygen at 320 K and a pressure of 15 atm. For oxygen, a 1.36 L2-atmimole2 and b = 0.003 183 L/mole. State your initial guess and solution with three significant digits Use the data from Computer Problem 11 to find the volume of 1 mole of benzene vapor at 700 K under a pressure of 20 atm. For benzene, a = 18.0 L2-atm/mole2 and b = 0.1 154 L/mole. 12. 3/(40)' 3 (b) Apply Newton's Method using an (a) Find the root of the function f(x) = (1 initial guess near the root, and plot the first 50 iterates. This is another way Newton's Method can fail, by producing a chaotic trajectory. (c) Why are Theorems 1.11 and 1.12 not applicable? 13. 4 6abx2 - 11b2 for your chosen values. Do not use a = 2, b-1/2, since that case already appears in Example 1.15. (b) Apply Newton's method to find both the negative root and the positive root of f(x). Then find intervals of positive initial guesses (d, d2], where d > di, for which Newton's Method: (c) converges to the positive root, (d) converges to the negative root, (e) is defined, but does 14. (a) Fix real numbers a, b> 0 and plot the graph of f(x) y initial guess where f"(x) = 0