Calculate f''(x) & Error Order | Numerical Analysis

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In summary, the conversation is about calculating a program using the equations f(x) and f'(x) with a given value of x, and finding the error order using the equation σ(h^2). The person asking wants a prompt response and clarification on whether or not the images provided show the work on the problem.
  • #1
quantum220
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write program calculate

[PLAIN]http://<a [/URL] href="http://www.codecogs.com/eqnedit.php?latex=f^{"}\left ( x \right )" target="_blank"><img src="http://latex.codecogs.com/gif.latex?f^{"}\left ( x \right )" title="f^{"}\left ( x \right )" /></a>[/PLAIN]
x=0
[PLAIN]http://<a [/URL] href="http://www.codecogs.com/eqnedit.php?latex=f\left ( x \right )=\frac{1}{sinx}" target="_blank"><img src="http://latex.codecogs.com/gif.latex?f\left ( x \right )=\frac{1}{sinx}" title="f\left ( x \right )=\frac{1}{sinx}" /></a>[/PLAIN]
the erroor order [PLAIN]http://<a [/URL] href="http://www.codecogs.com/eqnedit.php?latex=\sigma \left ( h^{2} \right )" target="_blank"><img src="http://latex.codecogs.com/gif.latex?\sigma \left ( h^{2} \right )" title="\sigma \left ( h^{2} \right )" /></a>[/PLAIN]
can you answer soon?
 
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  • #2
quantum220 said:
write program calculate

[PLAIN]http://<a [/URL] href="http://www.codecogs.com/eqnedit.php?latex=f^{"}\left ( x \right )" target="_blank"><img src="http://latex.codecogs.com/gif.latex?f^{"}\left ( x \right )" title="f^{"}\left ( x \right )" /></a>[/PLAIN]
x=0
[PLAIN]http://<a [/URL] href="http://www.codecogs.com/eqnedit.php?latex=f\left ( x \right )=\frac{1}{sinx}" target="_blank"><img src="http://latex.codecogs.com/gif.latex?f\left ( x \right )=\frac{1}{sinx}" title="f\left ( x \right )=\frac{1}{sinx}" /></a>[/PLAIN]
the erroor order [PLAIN]http://<a [/URL] href="http://www.codecogs.com/eqnedit.php?latex=\sigma \left ( h^{2} \right )" target="_blank"><img src="http://latex.codecogs.com/gif.latex?\sigma \left ( h^{2} \right )" title="\sigma \left ( h^{2} \right )" /></a>[/PLAIN]
can you answer soon?

Your images do not seem to be posting correctly. Can you provide direct links? Do your images show your work on the problem?
 
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What is the purpose of calculating f''(x)?

The second derivative, or f''(x), represents the rate of change of the slope of a function. This can be useful in determining the concavity of a curve, finding the maximum and minimum points of a function, and analyzing the behavior of a function near critical points.

What is numerical analysis?

Numerical analysis is a branch of mathematics that focuses on developing algorithms and methods for solving mathematical problems using numerical approximations. This field is essential for solving complex problems that cannot be solved analytically.

What is the error order in numerical analysis?

The error order refers to the rate at which the error in a numerical approximation decreases as the step size decreases. In other words, it measures how accurate a numerical method is.

How is f''(x) calculated numerically?

In numerical analysis, f''(x) is often approximated using finite difference formulas. These formulas use a finite step size, h, to estimate the second derivative at a given point x. The most common finite difference formulas for f''(x) are the three point endpoint formula and the three point midpoint formula.

Why is it important to analyze the error order of a numerical method?

The error order provides valuable information about the accuracy and efficiency of a numerical method. By understanding the error order, one can choose the most suitable method for a given problem and determine the optimal step size for achieving a desired level of accuracy.

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