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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;
Proof of: ∫ f(x) + g(x) dx = ∫ f(x) dx + ∫g(x) dx It is also a very easy proof. Assume that F(x) is an anti-derivative of f(x) and that G(x) is an anti-derivative of
Danielle requires knowing the distance around a basketball court. What geometry formula will she use? The perimeter of a rectangle is two times the length plus two times the wi
Explain the Graphical Technique of Linear Equations by using this figure.
Create a detailed diagram to describe the equation of an ellipse in terms of it’s eccentricity and indicate how the foci and major and minor semi-axes are involved. Y
Q. Multiplying Fractions Involving Negative Numbers? Ans. If you have only one negative sign, the result is still negative: If you have more than one, just remembe
Determine Rank Correlation Coefficient A group of 8 accountancy students are tested in Quantitative Techniques and Law II. Their rankings in the two tests were as:
From top of a tower a stone is thrown up and it reaches the ground in time t1. A second stone is thrown down with the same speed and it reaches the ground in t2. A third stone is r
Q. Converting Mixed Numbers to Improper Fractions? Ans. Converting a mixed number to an improper fraction is easy. A single multiplication, and then a single addition:
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
1/2+1/2
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