By means of sketches of the graphs y = 1/x and y = tan x, show that
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By means of sketches of the graphs y = 1/x and y = tan x, show that the equation x tan x = 1 has a root between x = 0 and x = 1/2π and an infinity of roots near x = kπ, where k = 1, 2, 3, . . . . . Deduce which of the two iterations
(a) xn + 1 = cot xn
(b) xn + 1 = tan−1(1/xn) + kπ
is convergent to the roots, and use it to locate the smallest positive root to 6dp.
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a b To 6 dp the root is 0860 334 Notice ...View the full answer
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