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Newton's Method : If xn is an approximation a solution of f ( x ) = 0 and if given by, f ′ ( xn ) ≠ 0 the next approximation is given by
xn+1 = xn - f(xn)/f'(xn)
It has to lead to the question of while do we stop? How several times do we go through this procedure? One of the more common stopping points in the procedure is to continue till two successive approximations agree upon a given number of decimal places.
t=w,w 2 L.H.S (w+w 2 ) + (w 2 + w) 2 ........ 1 + 1 ..... But every third term is of the form: (w 3n +w 3n ) 2 =22 There are nine such terms. Their sum is 36. The rema
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
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Variation of Parameters Notice there the differential equation, y′′ + q (t) y′ + r (t) y = g (t) Suppose that y 1 (t) and y 2 (t) are a fundamental set of solutions for
A computer is programmed to scan the digits of the counting numbers.For example,if it scans 1 2 3 4 5 6 7 8 9 10 11 12 13 then it has scanned 17 digits all together. If the comput
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Computing Limits :In the earlier section we saw that there is a large class of function which allows us to use to calculate limits. However, there are also several limits for whi
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Find the ratio in which the line segment joining A(6,5) and B(4,-3) is divided by the line y=2 (Ans:3:5) Ans : Let the ratio be k:1 x = 4 k + 6/ k +1 y
A polynomial satisfies the following relation f(x).f(1/x)= f(x)+f(1/x). f(2) = 33. fIND f(3) Ans) The required polynomial is x^5 +1. This polynomial satisfies the condition state
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