Write the raga lakshana of \(\textit{Pantuvarali.}\)
\(\textit{Pantuvarali}\) is a prominent and highly expressive raga in Carnatic music, known for its intense and meditative mood. It belongs to the 51st Melakarta raga in the Carnatic system. Key lakshanas (characteristics) of Pantuvarali:
Arohana (Ascending scale): Sa Ri1 Ga3 Ma2 Pa Dha1 Ni3 Sa
Avarohana (Descending scale): Sa Ni3 Dha1 Pa Ma2 Ga3 Ri1 Sa
Swara Variants: - Ri1: Sudda Rishabham (minor second) - Ga3: Antara Gandharam (major third) - Ma2: Prati Madhyamam (augmented fourth) - Dha1: Sudda Dhaivatam (minor sixth) - Ni3: Kakali Nishadam (major seventh)
Mood: Pantuvarali evokes feelings of devotion, pathos, and seriousness.
Usage: Often used in compositions expressing deep emotions, prayers, and meditative themes.
This raga is favored for its ability to convey both gravity and beauty in compositions and improvisations.
Explain the term \(\textit{Bhashanga}\) with examples such as Bhairavi, Kambhoji, etc
Find the interval in which $f(x) = x + \frac{1}{x}$ is always increasing, $x \neq 0$.