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Determine or find out if the following series is convergent or divergent.
Solution
In this example the function we'll use is,
f (x) = 1 / (x ln x)
This function is visibly positive and if we make x larger the denominator will obtain larger and thus the function is also decreasing. Hence, all we need to do is find out the convergence of the following integral.
The integral is divergent and thus the series is as well divergent by the Integral Test.
(a) Derive the Marshalian demand functions and the indirect utility function for the following utility function: u(x1, x2, x3) = x1 1/6 x2 1/6 x3 1/6 x1≥ 0, x2≥0,x3≥ 0
find the matrix of the linear transformations T:R2->R2 defined by T(x,y,z)=(x+2y,x-3z).
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The students of a class are made to stand in complete rows. If one student is more in each row, there would be 2 rows less, and if one student is less in every row, there would be
24x+7=3x+10
Evaluate the convergence of the algorithms: From the convergence proof of power method, LR and QR algorithm for the computation of eigenvalues we see that the easiest case to
G raph y = sec ( x ) Solution: As with tangent we will have to avoid x's for which cosine is zero (recall that sec x =1/ cos x) Secant will not present at
1. Show that there do not exist integers x and y for which 110x + 315y = 12. 2. If a and b are odd integers, prove that a 2 +b 2 is divisible by 2 but is NOT divisible by 4. H
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