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(1) Show that the conclusion of Egroff's theorem can fail if the measure of the domain E is not finite. (2) Extend the Lusin's Theorem to the case when the measure of the domain E
The Distributive Law : If you were asked to mentally multiply 37 with 9, how would you proceed? 1 would do it as follows - 37 is 30 + 7, 30 x 9 = 270, 7 x 9 = 63, so 270 + 63, th
what is -(-8)-(-4)*6-(-12)/4=
t=w,w 2 L.H.S (w+w 2 ) + (w 2 + w) 2 ........ 1 + 1 ..... But every third term is of the form: (w 3n +w 3n ) 2 =22 There are nine such terms. Their sum is 36. The rema
It is difficult to produce the individual answers and the insights that they were providing. But, let's look at some broad patterns that we found, which are similar to those that o
In order to compute the inequalities of the form where n 1 , n 2 , ....... , n k , m 1 , m 2 , ....... , m p are natural and real numbers and a 1 , a 2 , ... , a k ,
Geometric Applications to the Cross Product There are a so many geometric applications to the cross product also. Assume we have three vectors a → , b → and c → and we make
The ratio between the length and breadth of a rectangular field is 11:7. The cost of fencing it is Rs. 75,000. Find the dimensions of the field
Example of 3-D Coordinate System Example: Graph x = 3 in R, R 2 and R 3 . Solution In R we consist of a single coordinate system and thus x=3 is a point in a 1-D co
The two sides of a triangle are 17 cm and 28 cm long, and the length of the median drawn to the third side is equal to 19.5 cm. Find the distance from an endpoint of this median to
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