For which value of k, this funciton is continuous at x=1. f(x)= c… - Vidyadip

MCQ

For which value of $k$, this funciton is continuous at $x=1$.$ f(x)=\left\{\begin{array}{cc} \frac{x^2-3 x+2}{x-1}, & x \neq 1 \\
= k, & x=1 \end{array}\right. $

A
$1$
✓
$-1$
C
$0$
D
$3$

✓

Answer

Correct option: B.

$-1$

value of function at $x=1$
$f(1)=k$
Value of $\text{R.H.L.}$
$=\lim _{h \rightarrow 0} f(1+h)$
$=\lim _{h \rightarrow 0} \frac{(1+h)^2-3(1+h)+2}{1+h-1}$
$=\lim _{h \rightarrow 0} \frac{1+2 h+h^2-3-3 h+2}{h}$
$=\lim _{h \rightarrow 0} \frac{h^2-h}{h}$
$=\lim _{h \rightarrow 0}[h-1]$
$=-1$
because function is continuous at $x=1$, so
$f(1)= \text{R.H .L.}$
$\therefore k=-1$
Hence correct option is $(B).$

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