Consider the following recursive iteration scheme for different values of variable P with the initial guess x₁ = 1:

$${x_{n + 1}} = {1 \over 2}\left( {{x_n} + {P \over {{x_n}}}} \right)$$, n = 1, 2, 3, 4, 5

For P = 2, x₅ is obtained to be 1.414, rounded-off to three decimal places. For P = 3, x₅ is obtained to be 1.732, rounded-off to three decimal places. If P = 10, the numerical value of x₅ is __________. (round off to three decimal places)

The Fourier cosine series of a function is given by :

$$f(x) = \sum\limits_{n = 0}^\infty {{f_n}\cos nx} $$

For f(x) = cos⁴x, the numerical value of (f₄ + f₅) is _________. (round off to three decimal places)

The Cartesian coordinates of a point P in a right-handed coordinate system are (1, 1, 1). The transformed coordinates of P due to a 45$$^\circ$$ clockwise rotation of the coordinate system about the positive x-axis are

Let max {a, b} denote the maximum of two real numbers a and b. Which of the following statements is/are TRUE about the function f(x) = max{3 $$-$$ x, x $$-$$ 1}?