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Phenomena such as waiting times and equipment failure times are commonly modeled by exponentially decreasing probability density functions. Find the exact form of such a function.
The demand for a product, in dollars, is p = 2000-0.2x-0.01x2 find the consumer surplus when the sales level is 250
Find the length of cardioid r = 1+sin"\\theta"
Find the area of the region that lies inside the circle r = 3sin"\\theta" and outside the cardioid r = 1+sin"\\theta"
Find the Maclaurin series for the function f(x) = square root of
(x2+2-x)5
- integrate each of the following functions:
1.1 "\\int \\frac{dx}{x-\\sqrt{1-x^2}}"
1.2 "\\int" x * "sin^{-1}\\sqrt{x}dx" ( here "\\sin^{-1}" is the sine inverse).
When a particle is located a distance x meter from the origin, a force F( x )(newton) acts on it. Given F'(x) = 16.3.arctan(x - 8.5), F(8.5)=0. How much work is done in moving it from x=0 to x=8.5.
.
Sketch the region enclosed by the given curves. Decide whether to integrate with respect to x or y. Then find the area of the region.
2y = 4sqrt(x), y=5 and 2x + 2y =6.
There is a line through the origin that divides the region bounded by the parabola
y = 6x - 7x2 and the x-axis into two regions with equal area. What is the slope of that line?
Find the center of mass for each of the following regions.
1. The region bounded by y = x^3 ,x = -2 and the x-axis.
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