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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))`. Which one of the following statement is incorrect ?A. If L exist then a=1.B. If L does not exist then range of a is `[(1)/(12),1)uu(1,oo)`.C. `|f(x)|` is continuous and differentiable `AAx in R,AAainA`D. `f(|x|)` is non-derivable at exact,y two points. |
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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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