Explain the term \(\textit{Bhashanga}\) with examples such as Bhairavi, Kambhoji, etc
In Carnatic music, ragas are often classified based on their adherence to the parent melakarta scale. The term Bhashanga refers to a special category of janya ragas (derived ragas) that use one or more anya swaras (foreign notes), which do not belong to their parent melakarta scale.
Unlike upanga ragas, which strictly use notes only from their parent scale, Bhashanga ragas introduce external notes to enrich the melodic expression and emotional impact. These foreign notes give the raga a unique identity and allow for more nuanced improvisations.
Examples:
Significance:
Bhashanga ragas provide performers with greater scope for expression, allowing incorporation of subtle ornamentations and phrases that evoke different moods and rasas. They are extensively used in classical compositions and improvisations.
Write the raga lakshana of \(\textit{Pantuvarali.}\)
Find the interval in which $f(x) = x + \frac{1}{x}$ is always increasing, $x \neq 0$.