Apply Newton’s method on these test problems:
a. f (x) = x2.
Hint: The first derivative is zero at the root, and convergence may not be quadratic.
b. f (x) = x + x4/3.
Hint: There is no second derivative at the root, and convergence may fail to be quadratic.
c. f (x) = x + x2 sin(2/x) for x ≠ 0 and f (0) = 0 and f ′(x) = 1+2x sin(2/x)−2 cos(2/x) for x ≠ 0 and f ′(0) = 1.
Hint: The derivative of this function is not continuous at the root, and convergence may fail.
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