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Rule 1 The logarithm of 1 to any base is 0. Proof We know that any number raised to zero equals 1. That is, a 0 = 1, where "a" takes any value. Therefore, the loga
If the ratios of the polynomial ax 3 +3bx 2 +3cx+d are in AP, Prove that 2b 3 -3abc+a 2 d=0 Ans: Let p(x) = ax 3 + 3bx 2 + 3cx + d and α , β , r are their three Z
A set consists of (2n+1) elements. If the number of subsets of this set which consist of at most n elements is 8192. Find out the value of n. Ans: The following set has (2n + 1
I should have an account balance for $50.96. You took out $50.96 for a product on 6/18 which was NOT downloaded or delivered as it not available in the time frame I needed it. I am
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P and Q are the points (12,0) and (0,-5) respectively,find the length of the median through the origin O of the triangle OPQ
Seriation : You have read about a preschooler's ability to order. Ordering a set of objects means to arrange them in a sequence according to some rule. This arrangement could be
Fundamental Theorem of Calculus, Part I If f(x) is continuous on [a,b] so, g(x) = a ∫ x f(t) dt is continuous on [a,b] and this is differentiable on (a, b) and as,
Logarithmic Differentiation : There is one final topic to discuss in this section. Taking derivatives of some complicated functions can be simplified by using logarithms. It i
how do we solve multiple optimal solution
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