Let $f:(-a,a)\setminus\{0\} \to (0,+\infty)$.If $\lim(f(x)+\frac{1}{f(x)})=2$ ,then $\lim(f(x))=1$

Asked Aug 21 '20 at 07:16

Active Aug 21 '20 at 07:19

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Now the simple problem with these types of sums is that I am not getting any intuition and since I am not getting any intuition I am not able to try.Can anyone please give me some hints , and the geometric picture behind this?

edited Aug 21 '20 at 07:19

A learner

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asked Aug 21 '20 at 07:16

Antimony

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Limit at which point? Is it $0$?? – A learner Aug 21 '20 at 07:20
Hint set $\lim_{x\to ?}f(x)=\ell$. Then $\ell+\frac{1}{\ell}=2$. – Surb Aug 21 '20 at 07:20

Let $f:(-a,a)\setminus\{0\} \to (0,+\infty)$.If $\lim(f(x)+\frac{1}{f(x)})=2$ ,then $\lim(f(x))=1$

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