PirateFan308 said:I think I figured out a bit more. I have learned that I can split up the limit, so it will look like:
(lim3n+1)(lim7n+3) ÷ (lim4n)(lim5n-2)
and each of these individual limits equals +∞.
So I have +∞ ÷ +∞. Does this still equal infinity, 0, or does not exist?
A limit in terms of exponents with variables is a mathematical concept that describes the value that a function approaches as the input variable gets closer and closer to a specific value. In other words, it is the value that a function "approaches" but may not necessarily reach when the input variable gets infinitely close to a specific value.
To compute a limit with exponents and variables, you can use algebraic techniques such as factoring, simplifying, or combining like terms. You can also use graphical methods or numerical methods such as plugging in values to a table or calculator. In some cases, you may need to use more advanced techniques such as L'Hopital's rule or the squeeze theorem.
The common types of limits involving exponents and variables include polynomial limits, rational limits, radical limits, logarithmic limits, and exponential limits. These types of limits may involve different techniques for computing them, but the underlying concept remains the same.
The properties of limits with exponents and variables include the sum, difference, product, and quotient properties, as well as the power rule and the constant multiple rule. These properties allow us to simplify and evaluate more complex limits by breaking them down into smaller, more manageable parts.
Limits with exponents and variables are important in mathematics because they help us understand the behavior of functions and their graphs. They allow us to determine if a function is continuous at a certain point or if it has a horizontal or vertical asymptote. Limits are also crucial in calculus, as they are used to define derivatives and integrals.