Question

$\underset{x\to 0}{lim}\frac{x^{a}si{n}^{b}x}{sin\left(x^c\right)}$,a,b,b $\in$ R ~ {0} exists and has non-zero value, then

• A. a, b, c are in AP
• B. a, b, c are in GP
• C. a, b, c are in HP
• D. a+b=c

Answer 1

The correct option is D

a+b=c

= $\underset{x\to 0}{lim}{x}^{a+b-c}\frac{(\frac{sinx}{x}{)}^b}{\left(\frac{sin\left(x^c\right)}{x^c}\right)}$

The above limit has non-zero value only when