Solving Limit Questions: Expert Help with 3^x+4^x/7^x at Infinity

[student93]

Homework Statement

Lim (3^x+4^x)/(7^x) x -> ∞

Homework Equations

The Attempt at a Solution

I broke the limit up into two parts:

Lim (3^x)/(7^x) x -> ∞ + Lim (4^x)/(7^x) x -> ∞

However, I don't know where to go from here.

 

[Curious3141]

Homework Statement

Lim (3^x+4^x)/(7^x) x -> ∞

Homework Equations

The Attempt at a Solution

I broke the limit up into two parts:

Lim (3^x)/(7^x) x -> ∞ + Lim (4^x)/(7^x) x -> ∞

However, I don't know where to go from here.

Note that $\frac{3^x}{7^x} = (\frac{3}{7})^x$.

What's the limit of $a^x$ where $0 < a < 1$ as x goes to infinity?