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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 figure is made of a rectangle and an isosceles right triangle. the rectangle has sides of 6 in. and 3 in. one of the short sides of the rectangle is also one of the legs of the r
Evaluate following limits. Solution Let's begin with the right-hand limit. For this limit we have, x > 4 ⇒ 4 - x 3 = 0 also, 4 - x → 0 as x → 4
THE FIRST AND THIRD TERM OF A G.P ARE 8 AND 18 RESPECTIVELY AND THE COMMON RATIO IS POSITIVE.FIND THE COMMON RATIO
Two commuters leave the similar city at the same time but travel in opposite directions. One car is traveling at an average speed of 63 miles per hour, and the other car is traveli
what is the derivatives of y=u/5+7 and u=5x-35 using the chain rule?
Domain of a Vector Function There is a Vector function of a single variable in R 2 and R 3 have the form, r → (t) = {f (t), g(t)} r → (t) = {f (t) , g(t), h(t)} co
If A, B are acute angles and sinA= cosB, then find the value of A+B. Ans: A + B = 90 o
Application of Linear Equations We are going to talk about applications to linear equations. Or, put in other terms, now we will start looking at story problems or word probl
assigenment of b.sc.1sem
FORMULAS DERIVATION
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