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brojas7
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Homework Statement
Evaluate the anti derivative ∫e^x^2 dx as a Taylor Series
Homework Equations
[itex]\frac{f^(n)(a)}{n!}[/itex](x-a)^n
The Attempt at a Solution
Where do I start, I am not sure I understand the question
You need to include an attempt at solving the problem, before anyone can help you.brojas7 said:Homework Statement
Evaluate the anti derivative ∫e^x^2 dx as a Taylor Series
Homework Equations
[itex]\frac{f^{(n)}(a)}{n!}(x-a)^n[/itex]
The Attempt at a Solution
Where do I start, I am not sure I understand the question
brojas7 said:Homework Statement
Evaluate the anti derivative ∫e^x^2 dx as a Taylor Series
Homework Equations
[itex]\frac{f^(n)(a)}{n!}[/itex](x-a)^n
The Attempt at a Solution
Where do I start, I am not sure I understand the question
A Taylor Series is a representation of a function as an infinite sum of terms, with each term being a polynomial in the independent variable. It is used to approximate the value of a function at a given point by using information about the function's derivatives at that point.
Evaluating an antiderivative as a Taylor Series allows us to approximate the value of a function at a given point without having to use complicated integration methods. This can be particularly useful when dealing with complex or non-elementary functions.
To find the Taylor Series of an antiderivative, we use the Taylor Series expansion formula, which involves taking derivatives of the function at a given point and using those values to construct the terms of the series. The more terms we include in the series, the more accurate our approximation will be.
A Maclaurin Series is a special case of a Taylor Series, where the point we are approximating around is 0. In other words, a Maclaurin Series is a Taylor Series centered at x = 0. This means that the formula for a Maclaurin Series is simplified compared to a general Taylor Series.
No, a Taylor Series can only be used to approximate the value of a function at a point within a certain radius of convergence. This radius of convergence is determined by the properties of the function and the point we are approximating around. It is important to check the convergence of the series before using it to approximate a function's value.