1. Limited time only! Sign up for a free 30min personal tutor trial with Chegg Tutors
    Dismiss Notice
Dismiss Notice
Join Physics Forums Today!
The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

Limit at Infinity problem

  1. Apr 27, 2015 #1
    1. The problem statement, all variables and given/known data

    30uqyoh.png
    lim x->∞ (2^x-5^x) / (3^x+5^x)

    Choices :

    a. -1
    b. -2/3
    c. 1
    d. 6
    e. 25

    2. The attempt at a solution

    Hmmm.. I really have no idea about this.. This is an unusual problem..
    Please tell me...
     
  2. jcsd
  3. Apr 27, 2015 #2
    Try dividing numerator and denominator by something.
     
  4. Apr 27, 2015 #3

    Delta²

    User Avatar
    Gold Member

    Hint: nominator can be written as ##5^x((\frac{2}{5})^x-1)##. Also denominator can be written in a very similar way. Also i think you know that for any ##0<a<1## it is ##\lim\limits_{x \to +\infty}a^x=0##. If you use all this info i believe you should be able to find the correct answer.
     
  5. Apr 27, 2015 #4
    Hmm..
    I have no idea..
    By what something ?
    If I divide numerator and denominator by x, it will just make things more complicated
    Since the 2^x/x can't be simplified more... (The bad thing is the x is the exponent, not in the number)
     
  6. Apr 27, 2015 #5
    Use Delta2 hints and try writing the denominator.
     
  7. Apr 27, 2015 #6
    lim x->∞ 5^x((2/5)^x-1) / (5^x ((3/5)^x + 1))
    lim x->∞ (2/5)^x - 1 / ((3/5)^x + 1)
    -1/1 = -1

    Okay, I've got that the answer is a. -1
    Yeah, thanks for your hint :smile:
     
  8. Apr 27, 2015 #7

    HallsofIvy

    User Avatar
    Staff Emeritus
    Science Advisor

    Notice that this was the same as "divide both numerator and denominator by [itex]5^x[/itex]".
     
Know someone interested in this topic? Share this thread via Reddit, Google+, Twitter, or Facebook

Have something to add?
Draft saved Draft deleted



Similar Discussions: Limit at Infinity problem
Loading...