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Calculus
Show using the comparison test whether the integral of e^-x^2(sinx)dx is convergent or divergent on the interval [0,infinity].
Calculus
Suppose that, at a certain point, the pressure in a 500 cm3 piston chamber is 200 kPa, and rising at a rate of 10 kPa/second. At what rate is the volume decreasing?
Calculus
The total surface area S of a right circular cylinder is related to the base radius r and height h by the equation S=2πr2+2πrh
a) How is dS/dt related to dr/dt and dh/dt if neither r nor h is a constant?
b) How is dS/dt related to dr/dt if h is constant?
c) How is dS/dt related to dr/dt if r is constant?
a) How is dS/dt related to dr/dt and dh/dt if neither r nor h is a constant?
b) How is dS/dt related to dr/dt if h is constant?
c) How is dS/dt related to dr/dt if r is constant?
Calculus
The total surface area S of a right circular cylinder is related to the base radius r and height h by the equation S=2πr^2+2πrh
a) How is dS/dt related to dr/dt and dh/dt if neither r nor h is a constant?
b) How is dS/dt related to dr/dt if h is constant?
c) How is dS/dt related to dr/dt if r is constant?
a) How is dS/dt related to dr/dt and dh/dt if neither r nor h is a constant?
b) How is dS/dt related to dr/dt if h is constant?
c) How is dS/dt related to dr/dt if r is constant?
Calculus
linearization of e^(2x+1) at a=0
Calculus
one balloon can lift a basket containing items weighing at most 80 kg. two such balloons can lift the same basket containing items weighing at most 180 kg. what is the weight of basket?
Calculus
Use the chain rule to find the derivative of the function: y=(5x^3+4)^2. y'=?
Calculus
You are given a cone of height of 1 unit. The bas angle is 40 degrees. Determine what radius (of a perfect sphere) should have to maximize the volume within the cone. The volume above is irrelevant.
Calculus
whats 1990 times 1986
Calculus
You are an engineer in charge of designing the dimensions of a box-like building. The base is rectangular in shape with width being twice as large as length. (Therefore so is the ceiling.) The volume is to be 9000000 m3. Local bylaws stipulate that the building must be no higher than 50 m. Suppose the walls cost twice as much per m2 as the ceiling, and suppose the floor (i.e.base) costs nothing. Find the dimensions of the building that would minimize the cost.
Length is = ? m Width= ?m Height= ?m
Length is = ? m Width= ?m Height= ?m
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#340153 on Dec 2023
#340153 on Dec 2023