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Question Number 141356 by physicstutes last updated on 17/May/21
limx→+∞(x+1x2+1−1)
Answered by bemath last updated on 18/May/21
limx→∞(x+1−x2+1x2+1)=limx→∞(x(1+1x−1+1x2)x1+1x2)=limx→∞(1+1x−1+1x21+1x2)=0
Answered by Mathspace last updated on 18/May/21
f(x)=x+1x2+1−1⇒forx>0f(x)=1+1x1+1x2−1⇒f(x)∼1+1x1+12x2−1f(x)∼(1+1x)(1−12x2)−1=1−12x2+1x−12x3−1⇒f(x)∼1x−12x2→0(x→+∞)⇒limx→+∞f(x)=0
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