Question

Check whether limits are equal (LHL = RHL).....
1) f(x) = x+cosx
$\lim_{ x\to \ 0} f(x)$

Answer 1

$LHL:\ \lim_{x \to 0^{-}} \ \ x + cos\ x =\ \ 0^{-} + cos\ 0^{-} = 0 + 1 = 1 \\ \\ RHL:\ \ \lim_{x \to 0^{+}} \ \ x + cos\ x =\ \ 0^{+} + cos\ 0^{+} = 0 + 1 = 1$