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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;
sin 4 x - sin x = 0
What is the annual interest rate on an account in which earns $948 in simple interest over 36 months along with an initial deposit of $7,900? Using the easy interest formula In
Example of Partial Fraction Decomposition Evaluate the following integral. ∫ (3x+11 / x 2 -x-6) (dx) Solution: The 1 st step is to factor the denominator so far as
Now that we've found some of the fundamentals out of the way for systems of differential equations it's time to start thinking about how to solve a system of differential equations
A family may deduct 24% of their childcare expenses from their income tax owed. If a family had $1,345 in childcare expenses, how much can they deduct? Find out 24% of $1,345 b
Proves of power sets,union ,interstection ,relwtion
how do you find the length of a parallel line connecting two external circles of different sizes from the outside, given the value of both radius and one parallel line.
Method of cylinders or method of shells The formula for the area in all of the cases will be, A = 2 ∏ ( radius ) (heig
larry spends 3/4 hours twice a day walking and playing with his dog. He spends 1/6 hours twice a day feeding his dog. how much time does larry spend on his dog each day?
how can a curve be divided in three equal part?
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