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Using the method of cylindrical shells, set up an integral for the volume of the torus formed when the circle of radius 2 units covered at (3,0) is revolved about the line x=6
Factor the expression. Use the fundamental identities to simplify, if necessary. (There is more than one correct form of each answer.)
5 sin2(x) − 9 sin(x) − 2
Obtain a four-term Taylor polynomial approximation valid near x = 0 for each (1+ x)-⅓. Estimate the range of x over which three term polynomials will give two decimal accuracy.
Obtain a four-term Taylor polynomial approximation valid near x=,0 for each (1+x)^-1/3. Estimate the range of x over which three term polynomials will give two decimal accuracy
Evaluate the derivative lim┬(x→1)[1/(1-x) ∫_(x^2)^x▒(t^2-1)dt]
Evaluate the integration by substitution ∫▒〖1/√(1+√(1+x)) dx〗
Evaluate the integration by substitution ∫▒sin2θ/√(〖cos〗^2+16) dθ
Question 3: If the domain of 𝑓(𝑥)=3𝑎𝑥+22𝑏𝑥−1 is given by 𝐷={𝑥|𝑥∈ℝ,𝑥≠3} and the graph of this function passes through the point (−3,8). Write down the values of 𝑎 and 𝑏.
A door is submerged 5m in water. The dimensions of the gate are 5m by 4m wide.
a) the force of the water on the door
b) the distance of the centre of pressure from the surface.
c) If the door is hinged at the bottom of the door, calculate the moment the force produces about this hinge. Use ρ = 1000 kg/m3
Identify the missing number.
22, 22, 44, 1,
13, 3, 6, ?,
