Linear Approximation
Higher-Order Derivatives and Linear Approximation
Tangent Line Approximation / Linearization
Example:
Use a linear approximation to approximate the valve of each of the following:
a) sin(18π/17)
b) √15.9 Newton's Method
Basic idea of Newton's Method and how to use it.
One example using Newton's Method to approximate a root. Example:
Find where f(x) = x7 - 1000 intersects the x-axis; find solution correct to 8 decimal places. Newton's Method
Example:
Compute two iterations of Newton's method for the given function and indicated initial guess:
f(x) = x2 - 8, x1
Example:
Apply two iterations of Newton's method to approximate the x-value of a point of intersection of these two functions using the given initial guess:
f(x) = x2 - 4, g(x) = 2x - 3, x1 = 0
What is the value of x3? Newton's Method - How it Can FAIL
Example:
Given the following equation and initial guess, why would Newton's method fail to approximate a solution?
f(x) = (x - 2)2 - 1; x1 = 2
Rotate to landscape screen format on a mobile phone or small tablet to use the Mathway widget, a free math problem solver that answers your questions with step-by-step explanations.
You can use the free Mathway calculator and problem solver below to practice Algebra or other math topics. Try the given examples, or type in your own problem and check your answer with the step-by-step explanations.
We welcome your feedback, comments and questions about this site or page. Please submit your feedback or enquiries via our Feedback page.
