If $f: R \rightarrow R$ is defined by $f(x) = \left\{ {\begin{array}{*{20}{c}} {\frac{{x - 2}}{{{x^2} - 3x + 2}},}&{{\rm{ if \,\,}}x \in R - \{ 1,2\} }\\ {2,}&{{\rm{ if\,\, }}x = 1}\\ {1,}&{{\rm{ if\,\, }}x = 2} \end{array}} \right.$ then $\lim\limits _{x \rightarrow 2} \frac{f(x)-f(2)}{x-2}=$

JEE MATHEMATICS MCQ: DIFFERENTIATION

1 Easy

1 of 1

Application +4 | -1

f: R \rightarrow R

is defined by

f(x) = \left\{ {\begin{array}{cccccccccccccccccccc} {\frac{{x - 2}}{{{x^2} - 3x + 2}},}&{\mathrm{ if \,\,}x \in R - \{ 1,2\} }\\ {2,}&{\mathrm{ if\,\, }x = 1}\\ {1,}&{\mathrm{ if\,\, }x = 2} \end{array}} \right.

then

\lim\limits _{x \rightarrow 2} \frac{f(x)-f(2)}{x-2}=

View answer and explanation

Correct option: B

-1

Option B (-1) is correct because the limit of the difference quotient simplifies to -1 after factoring and canceling terms.