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

Answer

Proved

Explanation

(i) `f(0)=2`

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

$$
\begin{aligned}
&=\lim _{(x \rightarrow 0)}((sinx)/ x+\cos x) \\
&=1+1 \\
&=2
\end{aligned}
...