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What properties of a function can be discovered from its Maclaurin series?
Wiki User
∙ 13y ago
Yes. If the Maclaurin expansion of a function locally converges to the function, then you know the function is smooth. In addition, if the residual of the Maclaurin expansion converges to 0, the function is analytic.
Wiki User
∙ 13y ago
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Can properties of a function be discovered from its Maclaurin series Give examples.?
Best example is that an "odd" (or "even") function's Maclaurin series only has terms with odd (or even) powers. cos(x) and sin(x) are examples of odd and even functions with easy to calculate Maclaurin series.
How is pi 3.14 found?
The numerical value of pi is often found using a Taylor or Maclaurin series (Taylor series centered at 0).
How do you find the sum of a series of numbers?
There is no simple answer. There are simple formulae for simple sequences such as arithmetic or geometric progressions; there are less simple solutions arising from Taylor or Maclaurin series. But for the majority of sequences there are no solutions.
What is the use of successive differentiation?
There are several uses. For example: * When analyzing curves, the second derivative will tell you whether the curve is convex upwards, or convex downwards. * The Taylor series, or MacLaurin series, lets you calculate the value of a function at any point... or at least, at any point within a given interval. This method uses ALL derivatives of a function, i.e., in principle you must be able to calculate the first derivative, the second derivative, the third derivative, etc.
What is the difference between Taylor series and Maclaurin series?
A Maclaurin series is centered about zero, while a Taylor series is centered about any point c. M(x) = [f(0)/0!] + [f'(0)/1!]x +[f''(0)/2!](x^2) + [f'''(0)/3!](x^3) + . . . for f(x). T(x) = [f(c)/0!] + [f'(c)/1!](x-c) +[f''(c)/2!]((x-c)^2) + [f'''(c)/3!]((x-c)^3) + . . . for f(x).
Can properties of a function be discovered from its Maclaurin series Give examples.?
Best example is that an "odd" (or "even") function's Maclaurin series only has terms with odd (or even) powers. cos(x) and sin(x) are examples of odd and even functions with easy to calculate Maclaurin series.
What is a MacLaurins series?
A maclaurin series is an expansion of a function, into a summation of different powers of the variable, for example x is the variable in ex. The maclaurin series would give the exact answer to the function if the series was infinite but it is just an approximation. Examples can be found on the site linked below.
Why is it that if a equals 0 the Taylor's series becomes the maclaurin's series?
Simply because the Maclaurin series is defined to be a Taylor series where a = 0.
How is pi 3.14 found?
The numerical value of pi is often found using a Taylor or Maclaurin series (Taylor series centered at 0).
How do you find log values without Clark's table?
Unless the number happens to be a straightforward power of the base of the logs, the answer is that you cannot without some access to tables or a scientific calculator. There are Maclaurin series for the log function but without a powerful calculator, you will not get far with them.
How do you find the sum of a series of numbers?
There is no simple answer. There are simple formulae for simple sequences such as arithmetic or geometric progressions; there are less simple solutions arising from Taylor or Maclaurin series. But for the majority of sequences there are no solutions.
What is the use of successive differentiation?
There are several uses. For example: * When analyzing curves, the second derivative will tell you whether the curve is convex upwards, or convex downwards. * The Taylor series, or MacLaurin series, lets you calculate the value of a function at any point... or at least, at any point within a given interval. This method uses ALL derivatives of a function, i.e., in principle you must be able to calculate the first derivative, the second derivative, the third derivative, etc.
What is the difference between Taylor series and Maclaurin series?
A Maclaurin series is centered about zero, while a Taylor series is centered about any point c. M(x) = [f(0)/0!] + [f'(0)/1!]x +[f''(0)/2!](x^2) + [f'''(0)/3!](x^3) + . . . for f(x). T(x) = [f(c)/0!] + [f'(c)/1!](x-c) +[f''(c)/2!]((x-c)^2) + [f'''(c)/3!]((x-c)^3) + . . . for f(x).
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A company called Alexander Proudfoot Mining developed the Reactivity Series as a way of summarising all the different properties of the reactive metals as they were involved in extracting metals from ore
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