HELP PLEASE - harder EXTENSION 1 (limits) (1 Viewer)

cssftw

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Have no idea how to do this:

limit as n-->(infinity) OF (3^n + 5^n)^(1/n) --> just graphed it - it's a weird graph, the answer is 5 - can someone please show working out

help appreciated
 

Carrotsticks

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Consider the expression:



We know that if we omit the 3^n, we acquire the inequality:



We know that 3 < 5, so we have 3^n < 5^n.

If we were to put this into our expression, we acquire:



So combining our two inequalities yields:



So taking the limit as n approaches infinity, we acquire:




And so by the Squeeze Law, we have:



This is actually a specific case of this:

 
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RealiseNothing

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Consider the expression:



We know that if we omit the 3^n, we acquire the inequality:



We know that 3 < 5, so we have 3^n < 5^n.

If we were to put this into our expression, we acquire:



So combining our two inequalities yields:



So taking the limit as n approaches infinity, we acquire:




And so by the Squeeze Law, we have:



This is actually a specific case of this:

Love Squeeze Theorem/Law.
 

barbernator

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just put (3^99 + 5^99)^1/99 in calc :) so much easier hahaha... nah that law is awesome
 

deswa1

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just put (3^99 + 5^99)^1/99 in calc :) so much easier hahaha... nah that law is awesome
This is actually a good way to test whether you are correcct. Ideally though, use a bigger number :)
 

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