The function $f(x)=\left\{\begin{matrix}\frac{sinx}{x}+cosx, & if \, x≠0\\k, & if\, x=0 \end{matrix}\right.$ is continuous at x=0, then the value of k is :
Answer & explanation
Correct answer: option 1
The correct answer is Option (1) → 2
$f(0)=k$
$\underset{x→0}{\lim}f(x)=\underset{x→0}{\lim}\frac{\sin x}{x}+\cos x=1+1=2$
so $k=2$