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Consider the regression model Y i = a + bX i + u i , where the X i are non-stochastic and the u i are independently and identically distributed with E[u i ] = 0 and va
Properties 1. ∫ b a f ( x ) dx = -∫ b a f ( x ) dx . We can interchange the limits on any definite integral, all that we have to do is tack a minus sign onto the integral
use the expansion of (1-x)^7 to find the value of 1.998^7 correct to five significant figures
Explain Pie Charts ? If the frequencies are written as percentages, they can be easily compared using a pie chart. The following is an example of a pie chart using the data fr
area of r=asin3x
Grouping - situations in which we need to find the number of portions of a given size which can be obtained from a given quantity. (e.g., if there are 50 children in a class and t
(a) Find the curve on the surface z=x 3/2 joining the points(x,y,z)=(0,0,0) and (1,1,1) has the shortest arc lenght? (b) Use a computer to produce a plot showing the surface an
We here move to one of the major applications of differential equations both into this class and in general. Modeling is the process of writing a differential equation to explain a
Extreme Value Theorem : Assume that f ( x ) is continuous on the interval [a,b] then there are two numbers a ≤ c, d ≤ b so that f (c ) is an absolute maximum for the function and
A 10 m ladder of 150N is placed at an angle 30degrees to a smooth wall at point A and the other end (point B) on the ground. Assume that the weight of the ladder acts at its mid po
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