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Assume that (X, d) is a metric space and let (x1, : : : , xn) be a nite set of pointsof X. Elustrate , using only the de nition of open, that the set X\(x1, : : : , xn) obtained by removing every xi from X is open in X. (Sketch a picture to get some intuition!)
(a) Derive the Marshalian demand functions for the following utility function: u(x 1 ,x 2 ,x 3 ) = x 1 + δ ln(x 2 ) x 1 ≥ 0, x 2 ≥ 0 Does one need to consider the is
Determine if the following sequences are monotonic and/or bounded. (a) {-n 2 } ∞ n=0 (b) {( -1) n+1 } ∞ n=1 (c) {2/n 2 } ∞ n=5 Solution {-n 2 } ∞ n=0
A conical vessel of radius 6cm and height 8cm is completely filled with water. A sphere is lowered into the water and its size is such that when it touches the sides, it is just im
maths projects for class 11
If a differential equation does have a solution how many solutions are there? As we will see ultimately, this is possible for a differential equation to contain more than one s
table of 12
A 125-foot tower is located on the side of a mountain that is inclined at 32° to the horizontal. A guy wire is to be fitted to the top of the tower and anchored at a point 55 feet
Test Of Hypothesis On Proportions It follows a similar method to the one for means except that the standard error utilized in this case: Sp = √(pq/n) Z score is computed
Primary, note that quadratic is another term for second degree polynomial. Thus we know that the largest exponent into a quadratic polynomial will be a2. In these problems we will
Find out the general formula for the tangent vector and unit tangent vector to the curve specified by r → (t) = t 2 i → + 2 sin t j → + 2 cos t k → . Solution First,
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