classwork1

# classwork1 - t Write a formula for the manufacturer’s...

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Classwork I Sections 2.1 - 2.3 Consider the function f ( x ) = ± x 2 + 2 x if x ≤ - 1 cos( x ) if x > - 1 . Find f ( - 2), f ( - 1) and f (1). Let f ( u ) = 2 3 u - 2 . Find and simplify f ( x + h ) - f ( x ) h . What is the (natural) domain of r 3 x x 2 - 4 ? Let B ( c ) denote the area of the region bounded from above by the graph of the curve y = x (1 - x ), from below by the x -axis, and from the right by x = c . The domain of B is the interval [0 , 1]. Given that B (1) = 1 6 , ﬁnd B (0) and B ( 1 2 ) . (This is 2.1.39ab). Let ϕ ( x ) = x 3 - 2, ψ ( x ) = 3 x . Find: ( ϕ + ψ )( x ), ( ϕ ψ )( x ), ϕ 2 (2 x ) and ( ψ ϕ )( x + y ). Identify each of the following as odd functions, even functions or neither. Prove your claims. (This is 2.2.23). The sum of two even functions The sum of two odd functions The product of two even functions The product of two odd functions The product of an even function and an odd function After being in business for t years, a manufacturer of cars is making 120 + 2 t + 3 t 2 units per year. The sales price in dollars per unit has risen according to the formula 6000 + 700
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Unformatted text preview: t . Write a formula for the manufacturer’s yearly revenue R ( t ) after t years. (This is 2.2.28). Verify the following identities. (This is 2.3.12). • sin 2 v + 1 sec 2 v = 1 • cos 3 t = 4 cos 3 t-3 cos t • sin 4 x = 8 sin x cos 3 x-4 sin x cos x • (1 + cos θ )(1-cos θ ) = sin 2 θ Suppose that a high tide occurs at noon when the water level is 12 feet. Six hours later, a low tide with a water level of 5 feet occurs, and by midnight another high tide (12 feet) occurs. Assuming that the water level is periodic, ﬁnd a formula that gives the water level as a function of time. Then approximate the water level at 5:30 pm. (This is 2.3.58)....
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