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Practice upload — this tests the exact submission you’ll use on exam day. On a blank sheet of paper, hand-write your name and today’s date. Scan or photograph the page, save it as a single PDF, and upload that PDF using the file-upload box below. If the upload does not work, email Hang (hren5@gmu.edu) today.

Set up your webcam so that your face is fully visible. The viewer should not be 99% forehead or ceiling. Do not drop your head out of sight to view your notes. Raise your notes when viewing so there is no question as to whether you’re looking at a phone. Do not leave the test, close, or save a test as a draft during testing. Turn on the lights in your room – testing in darkness is pointless for Honorlock. Filters or blurred cameras are an integrity violation. You should be visible while testing. Not following any of the above regulations can result in a 0 grade for this test. ———–Test start: Test may only be taken once and must be finished in one sitting. Test is open now and will close at 10pm on the due date. You may take this test as soon as you finish the modules assigned. You must do this in order.Prep: Please ensure that you have used the restroom before starting, that your device is fully charged/plugged in, and that you have a strong internet connection. Test format:  The test is open note, meaning you may use one page front and back of written notes. You MUST EMAIL these to me in advance for approval. Monitoring: This test is monitored by Honorlock. Time limit: 90 minutesRestrictions: No googling, cell phones, AI, second screens or devices allowed. 

Formula sheet and tables attached at the end of the quiz. 

Find the first three nonzero terms of the power series solution centered at x=0 to the equation:    Recall that the power series expansion for

Find a minimum value for the radius of convergence of a power series solution about x=0 for 

Use the method of power series to determine the recurrence relation for the coefficients of the power series solution to the equation: 

Solve the initial value problem using the method of Laplace transforms. All steps must be shown. No credit will be given if solved with another method. 

Assume that the real interest rate increases, then the long-run price will , and long-run Real GDP will .  Assume that instead taxes decrease, then in the short-run the economy will experience a(n) .

Assume that an economy’s Investment into Capital = 545, Imports = 243, Exports =178, Government Spending = 440 (Assume no taxes).  If autonomous spending is $`value2`, and the marginal propensity to save is `value1`, then what will the Change in Real GDP be from a $`value3` increase in imports be (Include a negative (-) sign if negative, and round your answer to the nearest integer.  

If there is a $500 decrease in imports, then the new break-even level of real GDP will .  If disposable income remains at the old level, then after the decrease in imports it would now result in savings that are .  If the marginal propensity to consumer increases, then the effect of the $500 decrease in imports will (in absolue value).