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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;
a medical clinic performs three types of medical tests that use the same machines. Tests A, B,and C take 15 minutes, 30 minutes and 1 hours respectively, with respective profits of
Lines- Common Polar Coordinate Graphs A few lines have quite simple equations in polar coordinates. 1. θ = β We are able to see that this is a line by converting to Car
write a fortan programme to generate prime number between 1 to 100
4into 5 is;
Fundamental Theorem of Calculus, Part I As noted through the title above it is only the first part to the Fundamental Theorem of Calculus. The first part of this theorem us
Inverse Sine : Let's begin with inverse sine. Following is the definition of the inverse sine. y = sin -1 x ⇔ sin y = x for - ?/2 ≤ y ≤ ?/2 Hen
Extrema : Note as well that while we say an "open interval around x = c " we mean that we can discover some interval ( a, b ) , not involving the endpoints, such that a Also,
whats nine plus 10
Factor Expressions Involving Large Powers, Radicals, and Trig Functions You can use substitution to factor expressions involving large powers, radicals, and trig functions
AFIGURE THIS OUT(3) (14) (17) (20) (25)= 8 WHAT ARE THE PROCEDURES (-)(+)(x)(div) BETWEEN EACH NUMBER TO COME UP WITH 8 ?
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