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Let `f(x)=5-|x-2| and g(x)=|x+1|, x in R`. If f(x)n artains maximum value at `alpha` ang g(x) attains minimum value of `beta`, then `lim_(xto-alpha beta) ((x-1)(x^(2)-5x+6))/(x^(2)-6x+8)` is equal toA. `1//2`B. `-3//2`C. `-1//2`D. `3//2` |
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Answer» Correct Answer - A Given function are f(x)=-5-|x-2| and g(x) |x+1|, where `x in R`. Clearly, maximum of f(x) occurred at `x=2, so alpha, 2`. And minimum of g(x) occurred at `x=- 1, so beta=-1` `rArr alpha beta=-2` Now, `underset(x to- alpha beta) lim ((x-1)(x^(2)-5x+6))/(x^(2)-6x+8)` `underset(x to-2) lim ((x-1)(x-3)(x-2))/((x-4)(x-2))" " [ :. alpha beta =-2]` `underset(x to-2) lim ((x-1)(x-3))/((x-4))=((2-1)(2-3))/((2-4))=(1xx(-1))/((-2))=(1)/(2)` |
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