Calculus Answers

3. Find a polynomial, P(x), of degree 3 with zeros of 4,1 and −1, if P(0) = 8.

2. Let P (x) = 2x4 +15x3 +31x2 +20x +4

(a) Determine whether (x −1) is a factor of P (x). (2)

(b) Find all the possible rational zeros of P (x) by using the Rational Zeros Theorem. (2)

(c) Solve P (x) = 0

Find the moment about the x-axis of a wire of constant density that lies along The curve

𝑦 = √𝑥 from 𝑥 = 0 𝑡𝑜 𝑥 = 2

Find the Center of mass of a thin plate of constant density 𝛿 covering the region bounded by the parabola 𝑦 = 𝑥² and the line 𝑦 = 4.

Two Children balance on the seesaw. The 40 lb child is 5 ft from the fulcrum. How far from the fulcrum is the 50 lb child ?

A storage tank is a right circular cylinder 20 ft long and 8 ft in diameter with

its axis horizontal. If the tank is half full of olive oil weighing 57 lb/ft3, find the

work done in emptying it through a pipe that runs from the bottom of the

tank to an outlet that is 6 ft above the top of the tank.

A spring, whose unstretched length is 2.0 m is compressed to a length of 1/2 m

when a force of 10 N is applied. Find the work required to compress the spring

to a length of 1.0 m.