Hard limits problem (I think)

  • #1

Homework Statement



lim n->infinity (4^x + 7^x)^(1/x)

Homework Equations



Not applicable (?)

The Attempt at a Solution



Tried taking "plugging" infinity for n but I keep getting 1, is this right?

Seems too easy to be just 1?

Thank you.
 

Answers and Replies

  • #2
olivermsun
Science Advisor
1,248
118
1 isn't right.

Look at the thing being raised to the power 1/x. Which one will dominate as x gets large?
 
  • #3
2,571
1
Take the natural logarithm
 
  • #4
@olivermsun: The 4^x and 7^x will be bigger, but I am lost at the next step.

@flyingpig: Am I allowed to take the natural log of the function? Won't that change the limit?
 
  • #5
125
0
I think olivermsun is saying that one of those two terms will dominate as x gets larger.
 
  • #6
Delta2
Homework Helper
Insights Author
Gold Member
4,583
1,864
Find the limit of lnf(x), and then you can find the original limit as [tex]e^{limlnf(x)}[/tex]. Seems 7 to be the final answer.
 
  • #7
Ah thank you very much Delta, totally forgot about that part :)
 

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