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Homework Help: Limit at Infinity problem

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

    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


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    Homework Helper
    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
    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


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    Science Advisor

    Notice that this was the same as "divide both numerator and denominator by [itex]5^x[/itex]".
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