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mathematical formulaea b2 a2 b2 2aba - b2 a2 b2 - 2aba b2 a - b2 2a2 b2a
initial conditions and boundary conditionsin many problems on integration an initial condition y y0 when x 0 or a
if r per annum is the rate at which the principal a is compounded annually then at the end of k years the money due
we have seen that if y is a function of x then for each given value of x we can determine uniquely the value of y as per the functional
example suppose the demand and cost functions are given by q 21 - 01p and c 200
for the layman a function indicates a relationship among objects a function provides a model to describe a system economists
rule 1the logarithm of 1 to any base is 0proofwe know that any number raised to zero equals 1 that is a0 1 where a takes any value therefore
we know that 24 16 and also that 2 is referred to as the base 4 as the index or power or the exponent the same if expressed in terms of
consider this you have four units a b c and d you are asked to select two out of these four units how do you go about this particular
when three quantities a b and c are in gp then the geometric mean b is calculated as followssince these
learning geometric progression vis-aacute-vis arithmetic progression should make it easier in geometric progression also
when three quantities are in ap then the middle one is said to be the arithmetic mean of the other two that is if a b and
we know that the terms in an ap are given bya a d a 2d a 3d a n - 2d a n - 1dthe sum of all
a series is said to be in arithmetic progression ap if the consecutive numbers in the series differs by a constant value this
methodin this method we eliminate either x or y get the value of other variable and then substitute that value in either of the
before we look at simultaneous equations let us brush up some of the fundamentals first we define what is meant by an equation it is a
in this part we look at another method to obtain the factors of an expression in the above you have seen that x2 - 4x 4 x - 22 or
example factorize x2 - 4x 4if we substitute x 1 the value of the expression will be 12 - 41 4 1if we substitute x -1 the
above we have seen that 2x2 - x 3 and 3x3 x2 - 2x - 5 are the factors of 6x5 - x4 4x3 - 5x2 - x - 15 in this case we are able to find
example multiply 3x5 4x3 2x - 1 and x4 2x2 4the product is given by3x5 x4 2x2 4 4x3 x4 2x2 4 2x x4 2x2 4 - 1 x4
example 1add 4x4 3x3 - x2 x 6 and -7x4 - 3x3 8x2 8x - 4we write them one below the other as shown below 4x4
binomials trinomials and polynomials which we have seen above are not the only type we can have them in a single variable say
case 1 suppose we have two terms 8ab and 4ab on dividing the first by the second we have 8ab4ab 2 or 4ab8ab 12 depending on whether we consider