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lim n tends to infintiy ( {x} + {2x} + {3x}..... +{nx}/ n2(to the square) )where {X} denotes the fractional part of x?Ans) all no.s are positive or 0. so limit is either positive or 0.........(1)now {x}<=1;{2x}<=1;......{x}+{2x}+....{nx}<=nthat implies lim n tends to infinity{x}+{2x}+....{nx}/n^2 <= lmit n tends to infinity n/n^2;that means lim n tends to infinity{x}+{2x}+....{nx}/n^2 <= lmit n tends to infinity 1/n i.e. 0........(2)from (1) and (2);required limit=0;
What is the subset of {a,b,c}
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Write following in terms of simpler logarithms. (a) log 3 (9 x 4 / √y) Solution log 3 (9 x 4 / √y) =log 3 9x 4 - log y (1/2) =log 3 9 + log 3 x 4
Factoring polynomials Factoring polynomials is done in pretty much the similar manner. We determine all of the terms which were multiplied together to obtain the given polynom
Doing the following exercise will give you and opportunity to think about this aspect of children. E1) List some illustrations of exploration by four or five-year-olds that you
Two circles touch externally. The sum of their areas is 58 π cm 2 and the distance between their centres is 10 cm. Find the radii of the two circles. (Ans:7cm, 3cm) Ans:
jenna asked 100 of her schoolmates if they have had their first kiss and 43 of them said yes
Q. How to Add Fractions with Different Denominators? Ans. Here's the main thing to remember about adding fractions with different denominators-you can't! Fractions with di
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A rescue and ?re squad places a 15 ft ladder against a burning building. If the ladder is 9 ft from the base of the building, how far up the building will the ladder reach? a. 8
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