lim-n-x-2n-1-x-x-4n-

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 (\dots .) = 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 (\dots) = 0

i f / x / = 1 l i m (\dots) = \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 .