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lim-x-x-2-1-x-1-x-1-

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Question Number 121172 by benjo_mathlover last updated on 05/Nov/20
lim_(x→∞) (((√(x^2 +1))−x+1)/(x+1)) ?
limx→∞x2+1−x+1x+1?
Answered by TANMAY PANACEA last updated on 05/Nov/20
lim_(x→∞) ((x(√(1+(1/x^2 ))) −x+1)/(x+1)) lim_(x→∞) (((√(1+(1/x^2 ))) −1+(1/x))/(1+(1/x)))=(((√(1+0)) −1)/1)=0
limx→∞x1+1x2−x+1x+1limx→∞1+1x2−1+1x1+1x=1+0−11=0
Answered by Bird last updated on 05/Nov/20
f(x)=(((√(x^2 +1))−x+1)/(x+1)) ⇒ f(x)=((x(√(1+(1/x^2 )))−x+1)/(x+1)) ∼((x(1+(1/(2x^2 )))−x+1)/(x+1))=(((1/(2x))+1)/(x+1)) ⇒ lim_(x→+∞) f(x)=0
f(x)=x2+1−x+1x+1⇒f(x)=x1+1x2−x+1x+1∼x(1+12x2)−x+1x+1=12x+1x+1⇒limx→+∞f(x)=0

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