Taylor Inequality Error Calculator

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Formulas

The following formula is used to calculate the Taylor inequality error:

\[ E = \frac{|f^{(n+1)}(x)| \cdot r^{n+1}}{(n+1)!} \]

Where:

What is Taylor Inequality Error?

Taylor inequality error is an estimation of the error made when using a Taylor polynomial to approximate a function. It is based on the remainder term of Taylor's theorem, which provides a bound on the error. This error bound is useful for determining the accuracy of the approximation and for deciding how many terms of the Taylor series are needed to achieve a desired level of precision.

Example Calculation

Let's assume the following values:

Using the formula:

\[ E = \frac{|f^{(n+1)}(x)| \cdot r^{n+1}}{(n+1)!} \]

First, calculate the numerator:

\[ 50 \cdot 2^{4} = 50 \cdot 16 = 800 \]

Next, calculate the denominator (4!):

\[ 4! = 4 \times 3 \times 2 \times 1 = 24 \]

Finally, divide the numerator by the denominator to find the error:

\[ E = \frac{800}{24} \approx 33.33 \]

So, the Taylor inequality error is approximately 33.33.