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

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In summary, the given limit can be broken up into two parts: the limit of ##(\frac{3}{7})^x## as x goes to infinity and the limit of ##(\frac{4}{7})^x## as x goes to infinity. Since ##0 < \frac{3}{7} < 1## and ##0 < \frac{4}{7} < 1##, both limits will approach 0 as x goes to 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?
 

What is the concept of solving limit questions?

Solving limit questions involve determining the value that a function approaches as the input approaches a certain value, often infinity or negative infinity. This concept is important in calculus and is used to analyze the behavior of functions.

What is the formula for solving limit questions?

The formula for solving limit questions is lim (f(x))/g(x) = lim (f(x))/lim (g(x)), where f(x) and g(x) are functions and lim represents the limit as x approaches a certain value.

How do you solve limit questions using substitution?

To solve limit questions using substitution, you substitute the given value for x into the function and evaluate the resulting expression. This method is often used for simple limit questions.

What is the concept of infinity in solving limit questions?

Infinity is a concept used in solving limit questions that represents a value that is larger than any real number. As x approaches infinity, the function may approach a finite value, approach infinity itself, or oscillate between different values.

What is the role of expert help in solving limit questions?

Expert help in solving limit questions can provide guidance and assistance in understanding the concept and various methods for solving limit questions. They can also explain the application of limit questions in real-world scenarios and provide practice problems for better understanding.

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