scardizzle
Salve!
1.A unit square with the points ABCD, where A(1,0),B(1,1),C(2,1),D(2,0)
i) a line, l, passes through the origin with a gradient m and cuts the sides AB and CD at P and Q respectivley.
Comment on the possible values of m.
ii) For what value(s) of m does the line l, divide the area of the square in a ratio 2:1?
iii) Another line, k, passes through the origin with gradient, n, and cuts the square through sides AB and BS at S and T respectivley
Show that is it not possible for k to divide the area of the square in the ratio 2:1
2.Jaime wants to use Newton's Method to obtain the zero of x^1/3 = 0
i) using Newton's Method once with the first approximation of x = 1 to obtain a 2nd approximation
ii) using Newton's Method with a first approximation where x cannot = 0, show that the second approximation, x(2), is such that |x(2)| > |x|.
Explain the significance of this result.
All help is greatly appreciated.
i) a line, l, passes through the origin with a gradient m and cuts the sides AB and CD at P and Q respectivley.
Comment on the possible values of m.
ii) For what value(s) of m does the line l, divide the area of the square in a ratio 2:1?
iii) Another line, k, passes through the origin with gradient, n, and cuts the square through sides AB and BS at S and T respectivley
Show that is it not possible for k to divide the area of the square in the ratio 2:1
2.Jaime wants to use Newton's Method to obtain the zero of x^1/3 = 0
i) using Newton's Method once with the first approximation of x = 1 to obtain a 2nd approximation
ii) using Newton's Method with a first approximation where x cannot = 0, show that the second approximation, x(2), is such that |x(2)| > |x|.
Explain the significance of this result.
All help is greatly appreciated.
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