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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;
Optimization : In this section we will learn optimization problems. In optimization problems we will see for the largest value or the smallest value which a function can take.
(x+4)(x+6)>0
25 cookies have to be divided equally among 4 children.hw can we use elps to answer this question?
cos(x)y''+sin(x)y=2cos^3(x)sin(x)-1
applications of composit functions
1. (‡) Prove asymptotic bounds for the following recursion relations. Tighter bounds will receive more marks. You may use the Master Theorem if it applies. 1. C(n) = 3C(n/2) + n
Find the derivatives of the following functions a) y = 5x 4 +3x -1-x 3 b) y = (x+1) -1/2 c) y= e x2+1 d) y= e 3x lnx e) y =ln(x+1/x)y
Following are some examples of complex numbers. 3 + 5i √6 -10i (4/5) + 1 16i 113 The last t
3.6 in a fraction
find the value of x for which the distance between the points p(4,-5) and q(12,x) is 10 units
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