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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;
If the M-th term of an Ap is n andn-th term M.find the p-th term
Sin+cos
(a) An unordered pair fm; ng with 1 ≤ m ≠ n ≤ 6 is called a duad. List the 15 duads. (b) There are 15 ways to partition {1, ......, 6 } into 3 duads, such as { {1; 2}, {3, 4},
Evaluate following limits. Solution Here the first two parts are actually just the basic limits including inverse tangents and can easily be found by verifying the fol
Definite Integral : Given a function f ( x ) which is continuous on the interval [a,b] we divide the interval in n subintervals of equivalent width, Δx , and from each interval se
Center of Mass - Applications of integrals In this part we are going to find out the center of mass or centroid of a thin plate along with uniform density ρ. The center of mass
solution for this project
Topic : Use of Electronic whiteboards (ICT) in primary education in Australia and international. What are the key theories, concepts and ideas related to your topic? Wha
Brian's 100-yard dash time was 2.68 seconds more than one school record. Brian's time was 13.4 seconds. What is the school record? The school record is less than Brian's time.
Example of inflection point Determine the points of inflection on the curve of the function y = x 3 Solution The only possible inflexion points will happen where
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