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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;
Unit Normal Vector - Three Dimensional Space The unit normal vector is illustrated to be, N (t) = → T' (t) / (|| T → ' (t)||) The unit normal is orthogonal or normal or
no the parallel lines do not meet at infinity because the parallel lines never intersect each other even at infinity.if the intersect then it is called perpendicuar lines
What is the definition of Set?
1. Find the APY for the bank described below- A bank offers an APR of 4% compounded monthly. 2. Use the compound interest formula to compute the balance in the following a
It is the last case that we need to take a look at. Throughout this section we will look at solutions to the system, x?' = A x? Here the eigenvalues of the matrix A are compl
Example of Cartesian coordinate Graph: Example: The temperature of water flowing in a high pressure line was measured at regular intervals. Plot the subsequent recorded da
Definition of Relation A relation is a set of ordered pairs. It seems like an odd definition however we'll require it for the definition of a function though, before actuall
a group of 3o students is planning a thanksgiving party items needed hats @ $2.50 each.noise makers@$4.00 per pack of 5.Ballons @$5.00 per pack of 10.how many packs of noisemakers
Vector Form of the Equation of a Line We have, → r = → r 0 + t → v = (x 0 ,y 0 ,z 0 ) + t (a, b, c) This is known as the vector form of the equation of a line. The lo
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