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From a thin piece of cardboard 10 in. by 10 in., square corners are cut out so that the sides can be folded up to make a box. What dimensions will yield a box of maximum volume? What is the maximum volume? Round to the nearest tenth, if necessary.
A. 6.7 in. x 6.7 in. x 3.3 in.; 148.1 in³
B. 3.3 in. x 3.3 in. x 3.3 in.; 37 in³
C. 5 in. x 5 in. x 2.5 in.; 62.5 in³
D. 6.7 in. x 6.7 in. x 1.7 in.; 74.1 in³
Find the number of units that must be produced and sold in order to yield the maximum profit, given the following equations for revenue and cost:
R(x) = 30x - 0.5x 2
C(x) = 5x + 7.
A. 32 units
B. 26 units
C. 35 units
D. 25 units
Using the Epsilon and Delta definition, show that lim x approaching 2 for (3x-5) is =1
If f(x) = 2|x-1| and g(x) = 3x-10 , then f o g (1) = 12 .
True or false? Give reason.
Do the domain of the function f defined by √(3-x) /(x-2) is R - {2}
Find the domain and range of the function f defined by f(x) = 1/1-sinx
Find the following limits:
lim x approches 2 for x^2 + 4x -1/ x^2 -2x
Is the function f : R ➡R, defined by f(x) = 1-|x| is differentiable at x=1
a water tank in the form of an inverted cone is being emptied at the rate of 2 cubic feet per second. the height of the cone is 2.5m and the radius is 1.5m. find the rate of change of the water level when the depth is 2m. ( answer must be in english term)
Set-up the integral for the area A(R) of the region R bounded by the circles y
2 + x
2 = 1, and y
2 + x
2 = 4,
below the x-axis and to the left by the y-axis using the vertical strip.
