# Homework Help: Limit at Infinity problem

1. Apr 27, 2015

### terryds

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

2. Apr 27, 2015

### Raghav Gupta

Try dividing numerator and denominator by something.

3. Apr 27, 2015

### Delta²

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.

4. Apr 27, 2015

### terryds

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)

5. Apr 27, 2015

### Raghav Gupta

Use Delta2 hints and try writing the denominator.

6. Apr 27, 2015

### terryds

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
Notice that this was the same as "divide both numerator and denominator by $5^x$".