Prove that the function `f(x)={(sinx)/x,x<0,x+1,xgeq0` is everywhere continuous.

Explanation

`f(x)= {(sinx)/x` when `x<0` and `x+1` when `xge0`

For the continuity at `x=0`

`f(0)=1`

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

`text{LHL}=lim _{h -> 0} f({0}-h) `

`text{LHL}=lim _{h -> 0} (sin(0-h))/{0-h}`

`text{LHL} = lim _{h -> 0} (sin-h)/{-h}= 1`

Now,

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