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, $\lim _{x \rightarrow 1} f(x)=1$
Click here to get exam-ready with eSaral
For making your preparation journey smoother of JEE, NEET and Class 8 to 10, grab our app now.