mathematicalcircles

Thursday, 12 September 2013

The quadratic polynomial p(x) has the following properties:
p(x) is non-negative for all real numbers, p(1) = 0 & p(2) = 2.
compute p(0) + p(3)

let f be a linear function such that f(6) - f(2) = 12,
then compute f(12) - f(2) =

Find the fundamental period of the function
f(x) = cos (tan x + cot x) . cos (tan x - cot x)

f(f(x)) =x/2, f(x) = 2 x (2-x), x belongs to the closed intervals of 0 to 2

1. Y = sec x + (1/x), - π/2 < x < π/2

2. Y = tan x + (1/x⁴), - π/2 < x < π/2

Draw the graph of the following functions:-

1>> y = x + (x / mod x)

2>> y = sqrt (x) . sin(1/x)