Innequality prove question

  • Thread starter transgalactic
  • Start date
In summary, the conversation is about proving that the remainder, R_5, in the Maclaurin series for sin(x) is negative. The first three terms of the series are x-\frac{x^3}{6}+\frac{x^5}{120}, and the goal is to show that the remaining terms are smaller in absolute value compared to the first three terms.
  • #1
1,395
0
prove that..
[tex]
x-\frac{x^3}{6}+\frac{x^5}{120}>\sin x\\
[/tex]
[tex]
R_5=\frac{f^{5}(c)x^5}{5!}
[/tex]
i need to prove that the remainder is negative .
[tex]
\sin x=x-\frac{x^3}{6}+\frac{x^5}{120}+R_5
[/tex]
[tex]
R_5=\frac{cos(c)x^5}{5!}
[/tex]
 
Physics news on Phys.org
  • #2
I'm going to guess that you will use the Maclaurin series for sin(x) and cos(x).
 
  • #3
no?/////

i need to show that the remainder is negative??
 
  • #4
[tex]x-\frac{x^3}{6}+\frac{x^5}{120}[/tex]
These are the first three terms of the Maclaurin series for sin(x). Do you know what the terms immediately following them look like? Do you know how successive terms in this Maclaurin series compare in absolute value?
 

What is an inequality prove question?

An inequality prove question is a mathematical question that asks for the proof of a statement or inequality. It typically involves using mathematical equations and logic to show that the statement is true or false.

What is the purpose of an inequality prove question?

The purpose of an inequality prove question is to test a person's understanding of mathematical concepts and their ability to use logic and reasoning to prove a statement. It also helps to identify any gaps in knowledge and improve problem-solving skills.

What are some common strategies for solving inequality prove questions?

Some common strategies for solving inequality prove questions include using algebraic manipulation, substitution, and the properties of inequalities such as addition, subtraction, multiplication, and division. It can also be helpful to draw diagrams or use real-life examples to better understand the problem.

What are some common mistakes to avoid when solving inequality prove questions?

Some common mistakes to avoid when solving inequality prove questions include forgetting to consider all possible cases, making incorrect assumptions, and not showing all the steps in the proof. It's important to double-check all calculations and ensure that the proof is clear and concise.

How can I improve my skills in solving inequality prove questions?

To improve your skills in solving inequality prove questions, it's essential to practice regularly and seek help from a teacher or tutor if needed. It can also be helpful to review basic mathematical concepts and strategies, such as algebraic manipulation and the properties of inequalities, to build a strong foundation.

Similar threads

  • Calculus and Beyond Homework Help
Replies
3
Views
188
Replies
12
Views
146
  • Calculus and Beyond Homework Help
Replies
22
Views
1K
  • Calculus and Beyond Homework Help
Replies
4
Views
728
  • Calculus and Beyond Homework Help
Replies
9
Views
2K
  • Calculus and Beyond Homework Help
Replies
6
Views
469
  • Calculus and Beyond Homework Help
Replies
17
Views
321
  • Calculus and Beyond Homework Help
Replies
5
Views
2K
  • Calculus and Beyond Homework Help
Replies
21
Views
709
  • Calculus and Beyond Homework Help
Replies
3
Views
799
Back
Top