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Evaluate both of the following limits. Solution : Firstly, the only difference among these two is that one is going to +ve infinity and the other is going to negative inf
Evaluate following. ∫ 0 ln (1 + π ) e x cos(1-e x )dx Solution The limits are little unusual in this case, however that will happen sometimes therefore don't get
A radiograph is made of an object with a width of 3 mm using an x-ray tube with a 2 mm focal spot at a source-to-film distance of 100 cm. The object being imaged is 15 cm from the
(a) The generating function G(z) for a sequence g n is given by G(z) = 1 - 2z/(1 + 3z)3 Give an explicit formula for g n . (b) For the sequence gn in the previous part co
Logarithm Functions : Now let's briefly get the derivatives for logarithms. In this case we will have to start with the following fact regarding functions that are inverses of ea
The average age of a woman and her daughter is 16 years. The ratio of their ages is 7: 1. Then the woman''s age is
If OA = OB = 14cm, ∠AOB=90 o , find the area of shaded region. (Ans:21cm 2 ) Ans: Area of the shaded region = Area of ? AOB - Area of Semi Circle = 1/2 x 14 x
The sum of the squares of two consecutive positive odd integers is 74. What is the value of the smaller integer? Let x = the lesser odd integer and let x + 2 = the greater odd
A circular print is being matted in a square frame. If the frame is 18 in by 18 in, and the radius of the print is 7 in, what is the area of the matting? (π = 3.14) a. 477.86 in
Let A be an n×n matrix. Then Show that the set U = {u?R^n : Au = -3un} is a Subspace of R^n
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