Taylor series and quadratic approximation

Click For Summary
SUMMARY

The discussion focuses on using local quadratic approximation to estimate the square root of 36.03. The key method involves rewriting the expression as 6√(1+ε), where ε represents a small perturbation from 36. The participants emphasize expanding this expression to the second order of ε to achieve an accurate approximation. This approach effectively utilizes Taylor series concepts for practical calculations.

PREREQUISITES
  • Understanding of Taylor series expansion
  • Familiarity with quadratic approximation techniques
  • Basic knowledge of calculus, specifically derivatives
  • Ability to manipulate algebraic expressions
NEXT STEPS
  • Study Taylor series and its applications in approximation
  • Learn about local linear and quadratic approximations
  • Explore the concept of perturbation in mathematical analysis
  • Practice problems involving square root approximations using Taylor series
USEFUL FOR

Students studying calculus, mathematicians interested in approximation methods, and educators looking for practical examples of Taylor series applications.

ookt2c
Messages
16
Reaction score
0

Homework Statement



use an appropriate local quadratic approximation to approximate the square root of 36.03

Homework Equations



not sure

The Attempt at a Solution



missed a day of class
 
Physics news on Phys.org
ookt2c said:

Homework Statement



use an appropriate local quadratic approximation to approximate the square root of 36.03

Homework Equations



not sure

The Attempt at a Solution



missed a day of class

You need to rwwrite
\sqrt{36+0.03}
in the form 6 \sqrt{1+\epsilon} and then expand this to order epsilon squared. I will let you figure out what the value of epsilon is.
 

Similar threads

How should I show that this root is given approximately by this?
  • · Replies 2 ·
Replies
2
Views
2K
Link between Z-transform and Taylor series expansion
  • · Replies 2 ·
Replies
2
Views
2K
Taylor polynomial, approximative solution of this equation
  • · Replies 3 ·
Replies
3
Views
1K
Evaluate the Taylor series and find the error at a given point
  • · Replies 6 ·
Replies
6
Views
3K
Using a Taylor expansion to prove equality
  • · Replies 1 ·
Replies
1
Views
2K
Taylor Series Error Integration
  • · Replies 6 ·
Replies
6
Views
4K
[Calc II] quadratic Chebyshev approximation
  • · Replies 2 ·
Replies
2
Views
2K
How Does Including the Quadratic Term Affect the Newton Iteration Formula?
  • · Replies 1 ·
Replies
1
Views
2K
Find the limit using taylor series
  • · Replies 11 ·
Replies
11
Views
3K
What is the Taylor expansion of x/sin(ax)?
  • · Replies 5 ·
Replies
5
Views
3K