The following formula is used to calculate the Taylor inequality error:
\[ E = \frac{|f^{(n+1)}(x)| \cdot r^{n+1}}{(n+1)!} \]
Where:
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.
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.
