If `f(x)=(2x+3sinx)/(3x+2sinx)` , `x!=0` is continuous at `x=0` , then find `f(0)`

Explanation

`f(x)=frac{2 x+3 sin x}{3 x+2 sin x}`



If `f(x)` is continuous at `x=0`, then


`lim _{x -> 0} f(x)=f(0)`


`lim _{x -> 0} frac{2 x+3 sin x}{3 x+2 sin x}=f(x)`



`Rightarrow f(0)=lim _{x -> 0} frac{x(2+frac{3 sin x}{x})}{x(3+frac{2 sin x}{x})}`



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