InterviewSolution
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InterviewSolution
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Let `f(x)=ax^(2)+x+3andf(x)ge0AAx inR,AAainA" where "AsubR`. `"Also "L=Lim_(xto oo) (x+1-sqrt(ax^(2)+x+3))`. Range of a is equal toA. (0,1)B. `[1,oo)`C. `[(1)/(12),oo)`D. `(-oo,(1)/(12)]` |
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Answer» Correct Answer - A (i) `"As "ax^(2)+x+3ge0AAx inR` `"So, "agt0andDiscle0rArr1-12ale0rArr1le12arArrge(1)/(12)` `"So, "ain[(1)/(12),oo)`. (ii) `L=underset(xtooo)Lim(x+1-sqrt(ax^(2)+x+3))=L=underset(xtooo)Lim((x+1)^(2)-(ax^(2)+x+3))/((x+1)+sqrt(ax^(2)+x+3))=L=underset(xtooo)Lim((1-a)x^(2)(2a-1)x-2)/((x+1)+sqrt(ax^(2)+x+3))` `rArrL={{:(oo_(,),if,ain[(1)/(12)_(,))),((1)/(2)",",if,a=1),(-oo_(,),if,ain(1_(,)oo)):}` Now, werify alternatives. |
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