# Need help in determining the lim

• Equilibrium
In summary, the conversation is about finding the limit of a fraction as x approaches 4. The original poster is unsure about how to approach the problem, but other users suggest simply evaluating the limit by plugging in x=4, as there is no need to factor the polynomial. It is also mentioned that factoring would only be necessary if the function is not continuous or if plugging in x=4 would result in an undefined function.
Equilibrium
Hi

$$\lim_{x\rightarrow 4}\frac{x^2 - 3x + 4}{2x^2 - x - 1}$$

this is lim x ->4 which is the cube root of the whole fraction ^

Is there any way to answer this because i can't really factor it...

Last edited:
Why not just evaluate the limit at $x = 4$?

You don't need to factor it. It can easily be factored, since it's a ratio of quadratic polynomials.

Daniel.

Assuming f(x) is continuous at f(a) ($$\lim_{x \rightarrow a^{+}} f(x) = f(a) =\lim_{x \rightarrow a^{-}} f(x)$$) you can always just plug in a. The only time you would need to factor is if f(x) is not continuous at a or if plugging in a would result in an undefined function (0 in denominator). So yea, as courtigrad said, just substitute x=4. :-)

Last edited:

## What is a limit?

A limit is a fundamental concept in calculus that describes the behavior of a function as its input approaches a certain value. It represents the value that a function is "approaching" but never reaches, and can help us understand the overall behavior of a function.

## How do you determine the limit of a function?

To determine the limit of a function, we can either evaluate the function at values approaching the desired input value, or we can use algebraic techniques such as factoring and canceling to simplify the expression and find the limit. We can also use the properties of limits, such as the Sum, Difference, Product, and Quotient Rules, to find the limit of more complex functions.

## What are the common types of limits?

The common types of limits are limits at a point, limits at infinity, and one-sided limits. Limits at a point are used to describe the behavior of a function as it approaches a specific input value. Limits at infinity are used to describe the behavior of a function as its input approaches positive or negative infinity. One-sided limits are used to describe the behavior of a function as it approaches a specific input value from one direction.

## Why is it important to determine the limit of a function?

Determining the limit of a function is important because it helps us understand the overall behavior of the function, such as where it is increasing or decreasing, and whether it has any asymptotes or discontinuities. It is also a crucial concept in calculus, as it is used in the definition of derivatives and integrals.

## What are some real-world applications of limits?

Limits have many real-world applications in fields such as physics, engineering, economics, and biology. For example, in physics, limits are used to describe the motion of objects and the behavior of physical systems. In economics, limits are used to analyze the growth of a population or the rate of change of a market trend. In biology, limits are used to model the growth of a population or the concentration of a substance in a biological system.

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