Limit question

How do I find the limit of:

(3^x+4^x)/(4^x+5^x), as x tends towards infinity?

Thanks :smile:

Divide everything by 5^x.

Ok, that gives me (3^x+4^x)/(5^x.4^x+5^2x)

How does this help? :smile:

No, divide *everything* by 5^x (both top and bottom, so you don't change the actual value of the expression).

PeterR

Ok, that gives me (3^x+4^x)/(5^x.4^x+5^2x)

How does this help? :smile:

Dividing by 5^x gives

can you see how that helps?

multiply throughout by 5^x/5^x?

Edit: right ok, now I have just got rid of one of the power of x terms, how does that help?

Ah, so the limit will be zero because anything less than one (>-1) to the power of infinity = 0, so we get zero on top and 1 on the bottom?

You can't do say (1/2)^infinity. The limit is correct though.

How to revise for GCSE Psychology exams: AQA explains what to do

How to revise for GCSE Computer Science exams: AQA explains what to do

Your guide to handling revision and exam stress

How to revise for A-level Religious Studies exams: AQA explains what to do