Question
Iflimx→−∞(√x2−x+1−ax−b)=0 then the values of a and b are given by -
Answer: Option A
:
A
We have,limx→−∞(√x2−x+1−ax−b)=0[putting x=-y; x→−∞,y→∞]⇒limy→∞(√y2+y+1+ay−b)=0⇒limy→∞[y(1+1y+1y2)1/2+ay−b]=0⇒limy→∞[y{1+12(1y+1y2+.........)}+ay−b]=0⇒limy→∞[y(1+a)+(12−b)+12y+........]=0⇒1+a=0and(1/2)−b=0⇒a=−1andb=1/2
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:
A
We have,limx→−∞(√x2−x+1−ax−b)=0[putting x=-y; x→−∞,y→∞]⇒limy→∞(√y2+y+1+ay−b)=0⇒limy→∞[y(1+1y+1y2)1/2+ay−b]=0⇒limy→∞[y{1+12(1y+1y2+.........)}+ay−b]=0⇒limy→∞[y(1+a)+(12−b)+12y+........]=0⇒1+a=0and(1/2)−b=0⇒a=−1andb=1/2
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