Find the value

Question:

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

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

 

Solution:

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

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

$=5(1)-4$

$=5-4$

$=1$

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

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

$=4(1)^{3}-3(1)$

$=4-3$

$=1$

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

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

 

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