Create 2 planes including the following:

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Let f (x) = x e8x. find a formula for the nth derivative of f, where n is any positive integer. use x and n in your answer if needed. f (n)(x) =

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) = .

Which equation is true? i. 56 ÷ 4·7 = 82 ÷ (11 + 5) ii. (24 ÷ 8 + 2)3 = (42 + 9)2 neither i nor ii ii only i and ii i only