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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;
What is a truth table? Distinguish between Tautology & Contradiction?
if you start a business and john creates 6 t shirts more than pedro and pedro four t shirts less than eva and between the three of then made 22 tshirts, how many t-shirts made each
Polynomials In this section we will discuss about polynomials. We will begin with polynomials in one variable. Polynomials in one variable Polynomials in one variable
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So far we have considered differentiation of functions of one independent variable. In many situations, we come across functions with more than one independent variable
Jessica has a picture in a frame with a total area of 288 in2. The dimension of the picture without the frame is 12 in through 14 in. What is the larger dimension, in inches, of th
formules
x 4 - 25 There is no greatest common factor here. Though, notice that it is the difference of two perfect squares. x 4 - 25 = ( x 2 ) 2 - (5) 2 Thus, we can employ
Maxima and Minima We have to make a distinction between relative maxima (or minima) and global maxima (or minima). Let f(x) be a function of x. Then the global maxi
all basic knowledge related to geometry
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