Find the points of discontinuity, if any, of the following function: `f(x)={(sinx)/x\ \ \ ,\ \ \ if\ x<0 2x+3\ \ \ ,\ \ \ xgeq0`

Explanation

Case I:


If `c<0`, then `f(c)=frac{sin c}{c}` and `lim _{x -> c} f(x)=lim _{x -> c}(frac{sin x}{x})=frac{sin c}{c}` `therefore lim _{x -> c} f(x)=f(c)`


Therefore, `f` is continuous at all points `x`, such that `x<0`


Case II:


If `c>0`, then `f(c)=c+1` and `lim _{x -> c} f(x)=lim _{x -> c}(x+1)=c+1` `therefore lim _{x -> c} f(x)=f(c)`



Therefore, `f` is continuous at all points `x`, such that `x>0`


Case III:


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