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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;
evaluate limit as x approaches 0 (x squared times sin (1/x)
Use green's theorem to computer the integral F . dr where F = ( y^2 + x, y^2 + y) and c is bounded below the curve y= - cos(x),, above by y = sin(x) to the left by x=0 and to the r
How do I solve logx/log2x=2
write as a percent 6/10
y'' + 2y = 2 - e-4t, y(0) = 1 use euler''s method with a step size of 0.2 to find and approximate values of y
Evaluate following limits. Solution: Let's begin this one off in the similar manner as the first part. Let's take the limit of each piece. This time note that since our l
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For a first order linear differential equation the solution process is as given below: 1. Place the differential equation in the correct initial form, (1). 2. Determine the i
Jody's English quiz scores are 56, 93, 72, 89, and 87. What is the median of her scores? To find out the median, first put the numbers in sequence from least to greatest. 56, 7
The law of cosines can only be applied to acute triangles. Is this true or false?
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