yeah, that's why i am confusedlearningphysics said:Are you sure that's exactly the question? The limit approaches minus infinity...
EnumaElish said:The trick is to convert each term with x's into a term with 1/x's.
What do you need to divide with both the numerator and the denominator of the first term, to convert all the x's into 1/x's?
What do you need to divide with both the numerator and the denominator of the second term?
learningphysics said:Are you sure the question isn't:
[tex] \lim_{x \rightarrow \infty} ( \frac {3x^3}{(3x)^2-4}-\frac{x^2}{3x+2} ) [/tex]
f(x) said:I checked it again, but the question is exactly as I put it.
A limit in mathematics is a fundamental concept used to describe the behavior of a function as its input values approach a certain point. It is typically denoted by the symbol "lim" and can be thought of as the value that a function is approaching, but may not necessarily reach, as its input values get closer and closer to a specified value.
To evaluate a limit, you must first determine the function's behavior at the specified point and then use algebraic techniques, such as factoring and simplifying, to manipulate the expression until you can apply the limit definition. This may involve substituting the specified value into the function or using other limit properties and rules, such as the limit laws, to simplify the expression.
The limit definition, also known as the epsilon-delta definition, is a formal way of describing the concept of a limit. It states that the limit of a function f(x) as x approaches a value c is equal to L if for every positive number ε, there exists a positive number δ such that when the distance between x and c is less than δ, the distance between f(x) and L is less than ε.
The common types of limits include one-sided limits, where the input values approach the specified point from either the left or right side, and infinite limits, where the function approaches positive or negative infinity as the input values get closer to a certain point. Other types of limits include trigonometric limits, exponential limits, and logarithmic limits.
Limits are important because they allow us to understand and analyze the behavior of functions, especially when the function is undefined or has a discontinuity at a certain point. They also play a crucial role in calculus, as they are used to define derivatives and integrals, and are essential in solving many real-world problems in various fields such as physics, engineering, and economics.