Purchase Solution

Extrapolation formula for numerical derivative

Not what you're looking for?

Derive the extrapolation formula and show its error converges to zero more rapidly than does the error of (*).

Please see the attachment for the formula.

Solution Summary

We give a rigorous derivation of the extrapolation formula.

Solution Preview

If f(x) is twice differentiable, we have:

f(x+h) = f(x) + h f'(x) + h^2/2 f''(x) + o(h^2) (1)

where the "little o" error term o(h^2) denotes a function that goes to zero for h to zero, faster than h^2: For every epsilon > 0 there exists a delta>0 such that:

|o(h^2)| < epsilon h^2 when |h| < ...

Exponential Expressions

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

Graphs and Functions

This quiz helps you easily identify a function and test your understanding of ranges, domains , function inverses and transformations.

Geometry - Real Life Application Problems

Understanding of how geometry applies to in real-world contexts

Know Your Linear Equations

Each question is a choice-summary multiple choice question that will present you with a linear equation and then make 4 statements about that equation. You must determine which of the 4 statements are true (if any) in regards to the equation.

Probability Quiz

Some questions on probability