Find an error bound on e^x, fourth degree Taylor polynomial, illustrated with graphs!

In this video, we will learn how to find an error bound for e to the x using its fourth-degree Taylor polynomial about x equals zero. We will cover the concept of e sub n, which is the absolute value between a function and the nth degree polynomial. It will be less than or equal to m, an absolute value times x minus a raised to the n plus one over n plus one factorial, where m is a bound on the n plus first derivative of the function.

We will then apply this concept to e to the x, where we will expand it using a fourth-degree polynomial. We will show you the graph of the fifth derivative of e to the x, which is just e to the x. We will explain how to use any bound to find the error bound, and you can choose any bound as per your preference.

We will illustrate this using the graphs, where you can see the red line, which represents the absolute value of f of x minus t sub 4 of x. We will explain how we calculated the values using a bound of two and three, respectively.

By the end of this video, you will have a clear understanding of how to find an error bound on e to the x with a fourth-degree Taylor polynomial, and you will be able to use it to solve similar problems.

Keywords e sub n, error bound, Taylor polynomial, absolute value, nth degree polynomial, derivative, expansion, fourth-degree polynomial, fifth derivative, graphs, red line, black line, bound of two, bound of three, solve problems.

Tags #math #calculus #taylorpolynomial #errorbound #derivatives #absolutevalue #graphs #fourthdegree #fifthderivative #bounds #expansion #mathhelp

15 Common Internet Questions

1️⃣ What is e sub n in calculus?
Answer e sub n is the absolute value between a function and the nth degree polynomial.

2️⃣ What is a Taylor polynomial?
Answer A Taylor polynomial is a function that is used to approximate other functions in calculus.

3️⃣ How do you find the error bound in calculus?
Answer You can find the error bound in calculus by using the absolute value between a function and the nth degree polynomial.

4️⃣ What is the fifth derivative of e to the x?
Answer The fifth derivative of e to the x is just e to the x.

5️⃣ How do you use a fourth-degree Taylor polynomial to approximate e to the x?
Answer You can use a fourth-degree Taylor polynomial to approximate e to the x by expanding it using a fourth-degree polynomial.

6️⃣ What is the difference between a bound and an error bound in calculus?
Answer A bound is a limit on a function, while an error bound is the difference between a function and its approximation.

7️⃣ How do you find a bound in calculus?
Answer You can find a bound in calculus by calculating the absolute value of the n plus first derivative of a function.

8️⃣ What is the nth degree polynomial?
Answer The nth degree polynomial is a function that has a degree of n.

9️⃣ How do you calculate the factorial in calculus?
Answer You can calculate the factorial in calculus by multiplying a number by all the positive integers less than it.

🔟 What is the difference between a bound and a derivative in calculus?
Answer A bound is a limit on a function, while a derivative is the rate at which a function changes.

1️⃣1️⃣ How
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