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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;
Solve discrete harmonic mapping of a given surface patch (suppose the surface is genus-0 and with one boundary) 1. Map the boundary loop onto a unit rectangle using chord-length
into how many smaller part is each centimeter divided
how do you round to the nearest dollars?
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By the method of completion of squares show that the equation 4x 2 +3x +5 = 0 has no real roots. Ans: 4 x 2 +3 x +5=0 ⇒ x 2 + 3/4 x + 5 = 0 ⇒ x 2 + 3/4 x +
Probability Rules A probability is a number assigned to the occurrence of an event in a sample space. Probability measures must satisfy three rules. If A is an even
use the simplex method to solve the following lp problem. max z = 107x1 + x2 + 2x3 subject to 14x1 + x2 - 6x3 + 3x4 = 7 16x1 + x2 - 6x3 3x1 - x2 - x3 x1,x2,x3,x4 > = 0
Normally, sets are given in the various ways A) ROASTER FORM OR TABULAR FORM In that form, we describe all the member of the set within braces (curly brackets) and differen
Logarithm Functions : In this section we'll discuss look at a function which is related to the exponential functions we will learn logarithms in this section. Logarithms are one o
develop any two linear equation which are reducible into linear form from our daily life by cross multiplication
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