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Based upon past experience, barry expects no overdrafts. he expects no 2nd copies of statements. barry estimates that he will use network atms about 5 times a month with either bank. barry decides in the end to choose eecu. assuming that both banks provide the necessary services equally well, and based upon the tables of fees given above, how much can barry reasonably expect to save annually by choosing eecu in this case over e-town bank? a. $72 b. $78 c. $144 d. $24

Prove (a) cosh2(x) − sinh2(x) = 1 and (b) 1 − tanh 2(x) = sech 2(x). solution (a) cosh2(x) − sinh2(x) = ex + e−x 2 2 − 2 = e2x + 2 + e−2x 4 − = 4 = . (b) we start with the identity proved in part (a): cosh2(x) − sinh2(x) = 1. if we divide both sides by cosh2(x), we get 1 − sinh2(x) cosh2(x) = 1 or 1 − tanh 2(x) = .

What is always true about a positive integer raised to a negative odd power?