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Prove that, the complement of each element in a Boolean algebra B is unique. Ans: Proof: Let I and 0 are the unit and zero elements of B correspondingly. Suppose b and c b
If n is positive integer greater than 1 and a & b both are positive real numbers then, Consider that on occasion we can let a or b to be negative and yet have these propert
On 30 June 2012 Bill purchase a home by taking out a 30 year mortgage of $600,000 at 6% interest per annum, compounded months. Repayments are made at the end of each month. (a) Cal
Arc Length with Vector Functions In this part we will recast an old formula into terms of vector functions. We wish to find out the length of a vector function, r → (t) =
Proof for Absolute Convergence Very first notice that |a n | is either a n or it is - a n depending upon its sign. The meaning of this is that we can then say, 0 a n +
(a) Determine the matrix that first rotates a two-dimensional vector 180° anticlockwise, and then per- forms a horizontal compression of the resulting vector by a factor 1/2 (leavi
If (a,1/a), (b,1/b),(c,1/c),(d,1/d) are four distinct points on a circle of radius 4 units then,abcd is equal to?? Ans) As they are of form (x,1/x) let eq of circle be x
Squeeze Theorem (Sandwich Theorem and the Pinching Theorem) Assume that for all x on [a, b] (except possibly at x = c ) we have, f ( x )≤ h (
In the earlier section we looked at first order differential equations. In this section we will move on to second order differential equations. Just as we did in the previous secti
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