Integrals
Evaluate the integral of ∫(2x^2 −3)^2 dx
calculus
For the function f(x) = 3x2 − 5x − 7. Find the rate of change of f(x) at x = 3
statistics
Idiocracy. It's not a movie.
calculus
The marginal cost for a product is given by dC/dq = 1000/sqrt3q+20, in hundreds of dollars, where q is given in thousands of units. Determine the cost in dollars involved in increasing product from 10 to 15 thousand units. If R(0)= C(0)= 0, the marginal revenue is given by dR/...
Calculus
Fuel is flowing into a storage tank which can be filled to a depth of 6 metres. When the fuel started flowing the tank was already filled to a depth of 2.5m. If the rate at which the depth of fuel in the tank is increasing, in metres per hour is given by d'(t) = 4t +5, fin...
Calculus
Fuel is flowing into a storage tank which can be filled to a depth of 6 metres. When the fuel started flowing the tank was already filled to a depth of 2.5m. If the rate at which the depth of fuel in the tank is increasing, in metres per hour is given by d'(t) = 4t +5, fin...
Calculus
The marginal cost for a product is given by dC/dq = 1000/sqrt3q+20, in hundreds of dollars, where q is given in thousands of units. Determine the cost in dollars involved in increasing product from 10 to 15 thousand units. If R(0)= C(0)= 0, the marginal revenue is given by dR/...
Calculus
The acceleration due to gravity near the surface of Mars is 3.72ms^-2 . A rock is thrown straight up from the surface with an initial velocity of 23ms^-2 . How high does it go?
Calculus
Given f(x)=1+2cos x , find the area under the curve y=f(x) between x = pi/2 and 2pi/3.
Calculus
A cone is inscribed in a sphere of radius a, centred at the origin. The height of the cone is x and the radius of the base of the cone is r, as shown in the diagram opposite. Find the height, x, for which the volume of the cone is a maximum. (HINT: show that the volume of the ...
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