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}?

Consider the differential equation

$${{dy} \over {dx}} = 4(x + 2) - y$$

For the initial condition y = 3 at x = 1, the value of y at x = 1.4 obtained using Euler's method with a step-size of 0.2 is ________. (round off to one decimal place)