(1) For the function f(x) = 1 x²+1 (a) Find the derivative o...

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(1) For the function f(x) = 1 x²+1 (a) Find the derivative of f(x) (b) Find the domain of f(x) (c) Find the domain of f' (x) (2) Find the limit: limx 8 1 +4x4-2x - (3) Find derivative: dx d = dx d = = dx d = (2x - 3)2 (1 + tan (x2)) = ;; da dx d = and sin x e-x = (4) Find the antiderivative: f'(x) = sin(x) + x³ ;; = x2+2Vx f(1) = 0 (5) Find 'Y' (or dy/dx) using implicit differentiation: -y + x 2 = sin(xy) (6) Find the equation of the tangent line at (Tt/6, r/12) for (y)( x-tan x (7) Find the limit (use l'Hospital's Rule) limx->o 1-ex (8) Find the limit: use any method you prefer (9) Sketch f(x) following steps A through H of section 4.5 (You MUST show the details of every step clearly) f(x)= =2-2x (10)A piece of wire 20 m long is cut in two pieces as shown in the picture below. You must use the picture on next page for your calculations. The first piece is bent to a rectangle where the length is twice the width. The second piece is bent into a square. How could the wire be cut so the total area enclosed is: (a) maximum (b) minimum (See next page for details of geometry)

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