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Q.
Let f(x) = $\frac {x^4-5x^2+4} {|(x-1) (x-2)|}$ , x $\neq $ 1,2 = 6 ,x=1,12, x = 2, Then f (x) is continuous on the set
Solution:
$ f(x) = \frac {(x^2 - 1)(x^2-4)} {[(x-1) (x-2)]}$
Since $\lim_{x\to1} \frac{x-1}{\left|x-1\right|}$ does not exist.
$\lim_{x\to2} \frac{x-1}{\left|x-1\right|}$ does not exist.
$\therefore $ $\lim_{x\to1} f(x)$ and $\lim_{x\to2} f(x)$ do not exist.
$\therefore $ $f(x)$ is not continuous at $x$ = 1, 2 At all other points $f(x)$ is continuous
$\therefore $ $f(x)$ is continuous on R - {1, 2}.