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If `x=2` is a real root of cubic equation f (x) = `3x^(3)+bx^(2)+bx+3=0`. Then the value of lim_(xrarr(1)/(2)) (e^(f(x)-1)/(2x-1))`A. `(27)/(4)`B. `-(27)/(4)`C. `-(27)/(8)`D. `(27)/(8)` |
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Answer» Correct Answer - C `3x^(3)+bx^(2)+bx+3=3(x^(3)+1)+bx(x+1)=0` has roots `- 1,2,(1)/(2)` so, `underset(xrarr(1)/(2))(lim)((3x^(3)+bx^(2)+bx+3)/(2x-1))=(3(x-1)(x-2)(x-(1)/(2)))/(2(x-(1)/(2)))` `(3)/(2).(3)/(2).(-3)/(2)=-(27)/(8)` |
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