$\underset{x→-π}{\lim}\frac{|x+π|}{\sin x}$ is:
Answer & explanation
Correct answer: option 4
$\underset{x→-π}{\lim}\frac{|x+π|}{\sin x}$
$RHL = \underset{x→-π^+}{\lim}\frac{x+π}{\sin x}=\underset{h→0}{\lim}\frac{-π+h+π}{\sin(-π+h)}=1$
$LHL = \underset{x→-π^-}{\lim}\frac{x+π}{\sin x}=\underset{h→0}{\lim}\frac{(π+h-π)}{\sin(-π-h)}=-1$
$LHL≠RHL$ Limit does not exist.