If $\quad f: R \rightarrow R \quad$ is defined by $f(x)=[x-3]+|x-4|$ for $x \in R$, then $\lim _{x \rightarrow 3^{-}} f(x)$ is equal to

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Aicharya · Accepted Answer

Given that, $ \begin{aligned} f(x) & =[x-3]+|x-4| \ 	herefore \lim _{x ightarrow 3^{-}} f(x) & =\lim _{x ightarrow 3^{-}}([x-3]+|x-4|) \ & =\lim _{h ightarrow 0}([3-h-3]+|3-h-4|) \ & =\lim _{h ightarrow 0}([-h]+1+h) \ & =-1+1+0=0 \end{aligned} $

If $\quad f: R \rightarrow R \quad$ is defined by $f(x)=[x-3]+|x-4|$ for $x \in R$, then $\lim _{x…

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