Purchase Solution

Taylor's Theorem

Not what you're looking for?

Ask Custom Question

Please see the attached file for the fully formatted problems.

1 Write down the Taylor polynomial of , . Use Taylor's theorem to
show that =

2. Given that , 1 < e < 3. Do the followings.

a) Write down the Taylor polynomial of and show that for and

b) Use a) to show that for all c) Conclude that e is irrational?

Purchase this Solution

Solution Summary

Taylor's theorem are investigated.

Solution Preview

1. Proof:
Let , then , , and so on.
In general, we have . By Taylor's Theorem, we expand at and get . Especially, set , we have
.
2. Proof:
(a) Let , then and thus . By Taylor's Theorem, we ...

Purchase this Solution


Free BrainMass Quizzes
Geometry - Real Life Application Problems

Understanding of how geometry applies to in real-world contexts

Multiplying Complex Numbers

This is a short quiz to check your understanding of multiplication of complex numbers in rectangular form.

Solving quadratic inequalities

This quiz test you on how well you are familiar with solving quadratic inequalities.

Probability Quiz

Some questions on probability

Exponential Expressions

In this quiz, you will have a chance to practice basic terminology of exponential expressions and how to evaluate them.