Question

`lim_(xto0) (x^(a)sin^(b)x)/(sin(x^(c)))`, where `a,b,c inR~{0},` exists and has non-zero value. Then,

Answer 1

Correct Answer - C
`underset(xto0)lim(x^(a)sin^(b)x)/(sinx^(c))=underset(xto0)limx^(a)((sinx)/(x))^(b)((x^(c))/(sinx^(c)))x^(b-c)=underset(xto0)limx^(a+b-c)`
This limit will have non-zero value of `a+b=c.`