lim_(n→∞) (x^(2n) /(1+∣x∣+x^(4n) ))


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Question Number 27327 by Giannibo last updated on 05/Jan/18

$\lim_{n \to \infty} \frac{x^{2 n}}{1 + ∣ x ∣ + x^{4 n}}$
Commented by abdo imad last updated on 05/Jan/18

$= {l i m}_{n - >\propto} \frac{/ x /^{2 n}}{/ x /^{4 n} (/ x /^{- 4 n} + / x /^{- 3 n} + 1)}$ $= {l i m}_{n - >\propto} \frac{1}{/ x /^{2 n}} . \frac{1}{/ x /^{- 4 n} + / x /^{- 3 n} + 1}$
Commented by abdo imad last updated on 05/Jan/18

$l i m (. . . .) = 0$
Commented by prakash jain last updated on 05/Jan/18

$Does it matter if ∣ x ∣< 1 or ∣ x ∣> 1$ $or ∣ x ∣= 1 ?$
Commented by abdo imad last updated on 05/Jan/18

$y e s y e s i f / x / < 1 l i m (. . .) = 0$ $i f / x / = 1 l i m (. . .) = \frac{1}{3} i d o n t g i v e a t t e n t i o n t o t h i s c a s e .$
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