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Let $f(x)=5-|x-2|$ and $g(x)=|x+1|$ ,

$x\epsilon R$ . If $f(x)$ attains maximum value at $\alpha$ and $g(x)$ attains minimum

value at $\beta$ , then

$\lim_{x\rightarrow -\alpha \beta }\frac{(x-1)(x^{2}-5x+6)}{x^{2}-6x+8}$ is equal to :

Option 1)
$1/2$

Option 2)
$-3/2$

Option 3)
$-1/2$

Option 4)
$3/2$

Answers (1)

best_answer

Maxima of $f(x)$ occured at $x=2$ i.e. $\alpha =2$

Minima of $g(x)$ occured at $x=-1$ i.e. $\beta =-1$

$\therefore$ $\lim_{x\rightarrow 2}\frac{(x-1)(x-2)(x-3)}{(x-2)(x-4)}=\frac{1}{2}$

Option 1)

$1/2$

Option 2)

$-3/2$

Option 3)

$-1/2$

Option 4)

$3/2$

Posted by

Aadil

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