Relations and functions algebra 2

Explain why the function is discontinuous at the given number a. (select all that apply.) f(x) = 1 x + 1 a = −1 f(−1) is undefined. lim x→−1+ f(x) and lim x→−1− f(x) exist, but are not equal. lim x→−1 f(x) does not exist. f(−1) and lim x→−1 f(x) exist, but are not equal. none of the above

Which value is not a solution of 8x^3 – 1 = 0

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) = .