Graph the function defined by the parametric equations x = 2t3 – 3t and y = -2t2 – 1 over the parameter -2 < t < 2.

Ijust need to see how to do this. so you don’t have to answer all of them just a step by step explanation of one.

In the geometric progression –3, 12, −48… what term is 3,072?

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) = .