If `f(x)=f(x)={(sin(a+1)x+sinx)/(x^x c),x<0(sqrt(x+b x^2)-sqrt(x))/(b xsqrt(x)),xgeq0,x-0` is continuous at `x=0,t h e n` `a=-3/2,b=0,c=1/2` (b) `a=-3/2,b=1,c=-1/2` `a=-3/2,b in R-[0],c=1/2` (d) none of these

Explanation

Given,

`f(x)={(sin(a+1)x+sinx)/(x^x c)`

`f(0^-)=lim_(h->0){(sin(a+1)(0-h)+sin(0-h))/(-h)`

`f(0^-)=lim_(h->0){(sin(a+1)(h)+sin(h))/(h)`

`f(0^-)=((a+1)h+h)/(h)`

`f(0^-)=(a+2)`


Similarly,

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