What is the limit as n tends to infinity for the function 3n+1/7n-4?
The limit as n tends to infinity for the function 3n+1/7n-4 is 3/7. This is found by dividing the numerator and denominator by the highest power of n, which simplifies the function to (3+1/n)/(7-4/n). When n tends to infinity, terms 1/n and 4/n approach 0, simplifying the function to 3/7.
Understanding Limit as n Tends to Infinity
Limit is a fundamental concept in calculus that describes the value a function approaches as the input approaches a certain point. In this case, we are interested in finding the limit as n tends to infinity for the function 3n+1/7n-4.
When dealing with limits as n tends to infinity, we look at the behavior of the function as n becomes larger and larger. In the given function, as n approaches infinity, the leading terms become more significant in determining the overall value of the function.
To find the limit in this case, we apply the technique of dividing the numerator and denominator by the highest power of n, which helps simplify the function and determine the behavior as n tends to infinity.
In the function 3n+1/7n-4, dividing both the numerator and denominator by n results in (3+1/n)/(7-4/n). As n approaches infinity, the terms 1/n and 4/n become negligible, leading to the simplification of the function to 3/7.
Therefore, the limit as n tends to infinity for the given function is 3/7, indicating that the function approaches 3/7 as n becomes increasingly large.
For further learning on limits and their applications in calculus, you can explore more resources and practice problems to enhance your understanding of this fundamental concept.