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8. (a) Show that sinh-1 = ln(x + x2 + 1) Solution: Let y = sinh? 1. Then, 2 ev-e-y T = sinh y = - 2x = -e-y 0 = (eu)2 – 2xe" - 1 Then, by the Quadratic Formula we get 2x + e = - 4r2 + 4 -=IV2+1 2 Since, e > 0 we must have e = 1 + x2 +1 and so y=In(x + Vr2+1) [2] (b) Show that if f(x) = sinh-, then f'(x) = vez Solution: Using our answer from part (a) we get f(a) = + Ver #1 (1+ 2vmti) - z+Ve+I (+229 ) VEHI 1 =- 1 r2+1 x2 +1+1 Vr2 +1 I+ r2+1
3. Find the derivative of each function. a) f(x) = x b) g(x) = sec(z sinh ) c) h(x) = [ * sint di
6. Consider the function f(x) = (3-1) and "C) 2(x2 - 6) (a) [3 marks) Show that f'() = ? and f" (30) =
