Question

Check the continuity of $f\left(x\right)=\sin x+\cos x$ at $x=0$

Answer 1

$f\left(x\right)=\sin 0+\cos 0=1$

$\underset{x\to 0}{lim}f\left(x\right)=\underset{x\to 0}{lim}(\sin x+\cos x)=0+1=1$

$\Rightarrow$continuous.