Describe the term Kalpanaswaram.
Kalpanaswaram is an improvisational aspect of Carnatic music where the performer spontaneously creates sequences of swaras (musical notes) adhering to the rules of the raga and tala. It is typically performed after the main composition (kriti) to showcase the musician's creativity, knowledge, and mastery over melody and rhythm.
Key features of Kalpanaswaram include:
Kalpanaswaram is a vital and exciting feature of Carnatic concerts, offering an opportunity for creative exploration within strict classical frameworks.
Find the interval in which $f(x) = x + \frac{1}{x}$ is always increasing, $x \neq 0$.