Let fx-5-x-2- and gx-x-1- x- If fx attains maximum value at - and gx attains minimum value at - then limx-x-1x2-5x-6x2-6x-8 is equal to-

F(x) = 5 – |x – 2| f(x) attains maximum value when nbsp; |x – 2| = 0 ⇒ x = 2 = α nbsp; g(x) = |x + 1| g(x) attains minimum value when x = –1 = β lim_x→ αβ ...

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Byju's Answer

Standard XII

Mathematics

Factorization Method Form to Remove Indeterminate Form

Let fx=5-|x-2...

Question

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

\frac{1}{2}

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\frac{- 1}{2}

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\frac{3}{2}

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\frac{- 3}{2}

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Solution

The correct option is A $\frac{1}{2}$
$f (x) = 5 - | x - 2 |$
$f (x)$ attains maximum value when
$| x - 2 | = 0 \Rightarrow x = 2 = α g (x) = | x + 1 |$
$g (x)$ attains minimum value when $x = - 1 = β$
$lim x \to - α β \frac{(x - 1) (x^{2} - 5 x + 6)}{x^{2} - 6 x + 8} = lim x \to 2 \frac{(x - 1) (x - 2) (x - 3)}{(x - 2) (x - 4)} = \frac{1}{2}$

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Similar questions

Q. Let

f (x) = 5 - | x - 2 |

and

g (x) = | x + 1 |, x \in R .

f (x)

attains maximum value at

α

and

g (x)

attains minimum value at

β,

then

lim x \to - α β \frac{(x - 1) (x^{2} - 5 x + 6)}{x^{2} - 6 x + 8}

is equal to:

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f (x) = x^{2} - \frac{1}{x^{2}}

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g (x) = x - \frac{1}{x}, x \in R - - 1, 0, 1

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h (x) = \frac{f (x)}{g (x)}

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and

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f (x) = x^{2} + \frac{1}{x^{2}}

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g (x) = x - \frac{1}{x}, x ϵ R - {- 1, 0, 1}

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and

g (x) = x - \frac{1}{x},

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Let f(x)=5−|x−2| and g(x)=|x+1|,x∈R. If f(x) attains maximum value at α and g(x) attains minimum value at β, then limx→−αβ(x−1)(x2−5x+6)x2−6x+8 is equal to:

The correct option is A 12f(x)=5–|x–2| f(x) attains maximum value when |x–2|=0⇒x=2=αg(x)=|x+1| g(x) attains minimum value when x=–1=β limx→−αβ(x−1)(x2−5x+6)x2−6x+8=limx→2(x−1)(x−2)(x−3)(x−2)(x−4)=12

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