InterviewSolution
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InterviewSolution
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`lim_(x tooo)(sqrt(x^(2)+x+1)-x)` का मान ज्ञात कीजिए। |
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Answer» `lim_(xtooo)(sqrt(x^(2)+x+1)-x)=lim_(xtooo)((sqrt(x^(2)+x+1)-x)(sqrt(x^(2)+1+x)+x))/((sqrt(x^(2)+x+1)+x))` `=lim_(xtooo)(x^(2)+x+1-x^(2))/(sqrt(x^(2)+x+1)+x)=lim_(xtooo)(x+1)/(sqrt(x^(2)+x+1)x+)` `=lim_(xtooo)(x+1)/(sqrt(1+(1)/(x)+(1)/(x^(2))))=lim_(x to oo)(x(1+(1)/(x)))/(x(sqrt(1+(1)/(x)+(1)/(x^(2))+1)))` `=lim_(xtooo)(1+(1)/(x))/(sqrt(1+(1)/(x)+(1)/(x^(2))+1))=1/2` |
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