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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;
Let g be a function from the set G = {1,2,3,...34,35,36). Let f be a function from the set F = {1,2,3,...34,35,36}. Set G and F contain 36 identical elements (a - z and 0 - 9).
obtain the solution of y^4 +y=0
calculate x+2+y=4
Average Function Value The average value of a function f(x) over the interval [a,b] is specified by, f avg = (1/b-a) a ∫ b f(x) dx Proof We know that the average
What is Identities and Contradictions ? Look at this equation: x + 1 = 1 + x It happens to be true always, no matter what the value of x. (Try it out! What if x is 43?)
Children Learn From Each Other : The other day I had gone to a, nearby school to observe the teacher-children interaction. The children were working on a problem that the teacher
in a class of 55 students, 35 take english, 40 take french, and 5 take other languages.present this information in a venn diagam and determine how many students take both languages
what is 5 squared 2
Q. What is a percentage? Ans. Percent means "per hundred", or "out of 100". A percentage can be written as a ratio, or fraction, where the denominator (bottom) is 100.
The law of cosines can only be applied to acute triangles. Is this true or false?
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