[MATH 2A] - Final Exam Guide - Comprehensive Notes fot the exam (27 pages long!)

Math 115/Final (December 15, 2011) page 4 2. 6 points For each of the following statements, circle TRUE if the statement is always true and circle FALSE otherwise. Any ambiguous answers will be marked as incorrect. a. 12 points Suppose A(t) and B(t) are both everywhere differentiable functions which satisfy the equation A2 = eB for all real numbers t. If, additionally, In(2A(0)) = B(0), then A'(0) B(0) True False

Fall 2017 Math 2150 Final Exam Take 1 Part 1 Section 8 osed book, closed notes. No calculators. Show your work. No loitering, no smoking, walking on the grass, no feeding the animals, no parking, no stopping or standing, no mping, no running, no fishing, no vacancy. All problems weighted equally (1) Use Euler's method to estimate y(7) when y, + V-x and y(1) -3. Use step size 3. (2) Solve the differential equation (4xY + 3z2jdz + (3xY + 6y2)dy 0. 3) Is the differential equation y'"-6z3y" cosas linear? why or why not? 4) Tanks T1 and T2 contain 50 gallons and 100 gallons of salt solutions, respectively. A solution with 2 pounds of salt per gallon is pumped into T1 from an external source at 1 gal/min, and a solution with 3 pounds of salt per gallon is pumped into T2 from an external source at 2 gal/min. The solution from T1 is pumped into T2 at 3 gal/min, and the solution from T2 is pumped into T1 at 4 gal/min. T1 is drained at 2 gal/min and T2 is drained at 1 gal/min. Let Q1(t) and Q2(t) be the number of pounds of salt in T1 and T2, respectively, at time t>0. Derive a system of differential equations for Q1 and Q2. Assume that both mixtures are well stirred. guess" method (a kn

Fall 2017 Math 2150 Final Exam Take 1 Part 2 Section 8 Closed book, closed notes. No caleulators. Show your work. No loitering, no smoking, no walking on the grass, no feeding the animals, no parking, no stopping or standing, no dumping, no running, no fishing, no vacancy. All problems weighted equally. (1) Use the power series method to solve (1-z)y" +zy-y = 0. Here's a standard power series that you will find useful in your answer: 23 2 3 4! n! nao (2) A 64 Ib object stretches a spring 4 ft in equilibrium. It is attached to a dashpot with damping constant c-8 lb-sec/ft. The object is initially displaced 18 inches above equilibrium and given a downward velocity of 4 ft/sec. Find its displacement for t>0. Assume the motion is free. Since the weight is 64, for the mass you can use m =64/32 = 2. The following equations will be useful: The equation of motion for this system is my" + c/ + ky= F, where m is the mass of the object, c is the damping constant, k is the spring constant, and F is the forcing function. mg = kar, where g 32n/s2 is the gravitational constant, and Al is the distance by which a spring is stretched from its natural length when the object is attached to it. Remember to convert from inches to feet, so all units are compatible.