Which is a valid prediction about the continuous function f(x)?
a. f(x) ≥ 0 over the interval [5, ∞).
b. f(x) ≤ 0 over the interval [–1, ∞).
c. f(x) > 0 over the interval (–∞, 1).
d. f(x) < 0 over the interval (–∞. –1).

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) = .