Question

Let $f(x) = 5- |x-2| $ and $g(x) = |x + 1|, x \in$ R. If $f(x)$ attains maximum value at $\alpha$ and $g(x) $ attains minimum value at $\beta$, then $\displaystyle\lim_{x\to-\alpha\beta} \frac{(x-1)(x^2 -5x+6)}{x^2 - 6x + 8}$ is equal to :

• A. 1/2
• B. -3/2
• C. 3/2
• D. -1/2

Answer 1

Answer: (A)

Maxima of $f(x)$ occured at $x = 2$ i.e. $\alpha$ = $2$
Minima of g(x) occured at $x = -1$ i.e. $\beta$ = $-1$
$\therefore \, \, \lim_{x \to 2} \, \, \frac{(x-1)(x-2)(x-3)}{(x-2)(x-4)} = \frac{1}{2}$