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)

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

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