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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;
Melissa is four times as old as Jim. Pat is 5 years older than Melissa. If Jim is y years old, how old is Pat? Start along with Jim's age, y, because he appears to be the young
i dont now how to do it
1/2 + 2/8 =
G raph y = sec ( x ) Solution: As with tangent we will have to avoid x's for which cosine is zero (recall that sec x =1/ cos x) Secant will not present at
Solve cos( 4 θ ) = -1 . Solution There actually isn't too much to do along with this problem. However, it is different from all the others done to this point. All the oth
Place ten pebbles (or any other such objects) in front of a child who can recite number names upto ten in the correct sequence. Ask him/her to count them aloud while touching the p
Direction Cosines This application of the dot product needs that we be in three dimensional (3D) space not like all the other applications we have looked at to this point.
x2+y2 r=12
Explain Different Base Numbers? In multiplying or dividing two exponential expressions with different base numbers, write out the exponential expressions as products. Since
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