Prove that


Let $f(x)=\left\{\begin{array}{l}4 x-5, x \leq 2 \\ x-a, x>2\end{array}\right.$

If $\lim _{x \rightarrow 2} f(x)$ exists then find the value of $a$.



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

$\lim _{x \rightarrow 2^{-}} f(x)=\lim _{x \rightarrow 2^{-}} 4 x-5$




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

$\lim _{x \rightarrow 2^{+}} f(x)=\lim _{x \rightarrow 2^{+}} x-a$


Since $\lim _{x \rightarrow 2} f(x)$ it exists,

$\lim _{x \rightarrow 2^{-}} f(x)=\lim _{x \rightarrow 2^{+}} f(x)$

$\rightarrow 3=2-a$

$\rightarrow a=2-3$

$\rightarrow a=-1$


Leave a comment


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.

Download Now