Find the value


Let $f(x)=\left\{\begin{array}{l}5 x-4, \quad 0

Find $\lim _{x \rightarrow 1} f(x)$



Left Hand Limit(L.H.L.):

$\lim _{x \rightarrow 1^{-}} f(x)=\lim _{x \rightarrow 1^{-}} 5 x-4$




Right Hand Limit(R.H.L.):

$\lim _{x \rightarrow 0^{+}} f(x)=\lim _{x \rightarrow 0^{+}} 4 x^{3}-3 x$




$\therefore \lim _{x \rightarrow 0^{-}} f(x)=\lim _{x \rightarrow 0^{+}} f(x)$

Thus, $\lim _{x \rightarrow 1} f(x)=1$


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