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

#### cssftw

##### Member
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

##### Retired

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:

Last edited:

#### RealiseNothing

##### what is that?It is Cowpea

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.

##### Cult of Personality
Love Squeeze Theorem/Law.
*cough*Pinching Theorem*cough*

But yes, this kinda proves once again that Harder 3u can be the most difficult topic in MX2.

#### barbernator

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

#### deswa1

##### Well-Known Member
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 #### barbernator

##### Active Member
This is actually a good way to test whether you are correcct. Ideally though, use a bigger number my calc gives 5 by using that anyway 