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how are and calculated if p is a polynomial function ?

**How are lim p(x) and lim p(x) calculated if p is a polynomial function?**

As we delve into the world of calculus, we often come across the concept of limits. One important question that arises is how to calculate the limits of a polynomial function. In this post, we will explore the answer to this question and discuss the properties of polynomial functions that make them unique.

**What is a polynomial function?**

A polynomial function is a function that can be written in the form:

P(x) = anxn + … + a1x + a0

where an, a1, …, a0 are real numbers and n is a non-negative integer. In other words, a polynomial function is the sum of one or more terms, each of which is a constant multiplied by a variable raised to a non-negative integer power.

**Calculating limits of polynomial functions**

Now, let’s focus on calculating the limits of a polynomial function. The problem we’re interested in is finding the limit of p(x) as x approaches a, denoted by limx→a p(x). To calculate this limit, we must first check if p(x) is a polynomial function.

**Properties of polynomial functions**

Polynomial functions have several important properties that make them easy to work with. For example:

* If you add or multiply two polynomial functions, the result is also a polynomial function.
* Polynomial functions can be graphed as smooth, continuous curves.

Given these properties, it’s clear that polynomial functions are well-behaved and can be easily manipulated. In fact, the limit of a polynomial function as x approaches a is equal to the value of the function at x=a.

**Conclusion**

In conclusion, calculating the limits of polynomial functions is a straightforward process that requires a basic understanding of the properties of polynomial functions. By recognizing that polynomial functions are well-behaved and can be graphed as smooth, continuous curves, we can easily calculate the limits of these functions. Whether you’re studying calculus or simply need to understand the basics of functions, this knowledge will serve you well.

**Additional resources**

For more information on polynomial functions and limits, check out the following resources:

* [Chegg](https://www.chegg.com) for a detailed solution to the problem of calculating the limits of a polynomial function.
* [CliffsNotes](https://www.cliffsnotes.com) for a study guide on polynomial functions.
* [Symbolab](https://www.symbolab.com) for an online calculator that can help you determine if a function is a polynomial.
* [OpenStax](https://openstax.org) for a comprehensive textbook on college algebra.
* [Cuemath](https://www.cuemath.com) for a detailed explanation of polynomial functions and their properties.

**Quizlet**

For a fun and interactive way to practice calculating limits of polynomial functions, check out the following Quizlet:

* [If p is a polynomial, show that limx→a p(x) = p(a)](https://quizlet.com/explanations/questions/if-p-is-a-polynomial-show-that-c1eab004-54c7-4327-a215-c8df9b225776)

**YouTube Video**

Watch this YouTube video to learn more about polynomial functions and limits:

* [Polynomial Functions and Limits](https://www.youtube.com/watch?v=POdNjomXHWA)