Show that the function `f(x)` given by `f(x)={(sinx)/x+cosx ,\ \ x!=0 2,\ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ x=0` is continuous at `x=0` .

Explanation

(i) `f(0)=2`


(ii) `lim _{(x rightarrow 0)} f(x)`



`=lim _{(x rightarrow 0)}(sin x / x+cos x) `

`
=1+1 `

`
=2`



(iii) `lim _{(x rightarrow 0)} f(x)=2=f(0)`


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