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

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SUMMARY

The limit of the expression (3^x + 4^x) / (7^x) as x approaches infinity can be simplified by breaking it into two parts: Lim (3^x)/(7^x) and Lim (4^x)/(7^x). Each part can be rewritten as (3/7)^x and (4/7)^x, respectively. Since both bases, 3/7 and 4/7, are less than 1, their limits approach 0 as x approaches infinity. Therefore, the overall limit is 0.

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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.
 
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student93 said:

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?
 

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