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Sergeu [11.5K]
1 year ago
7

Find the maclaurin series for f(x) using the definition of a maclaurin series. [assume that f has a power series expansion. do n

ot show that rn(x) → 0. ] f(x) = e−6x
Mathematics
1 answer:
Nady [450]1 year ago
4 0

The equation of f(x) = e^{-6x} by maclaurin series is f(x)=\sum_{i=0}^{\infty} \frac{(-6.x)^{i}  }{i!}.

The maclaurin series for f(x) is defined by the following formula:

f(x) = \sum_{i=0}^{\infty} \frac{f^{(i)} (0)}{i!} .x^{i}--------------(1)

Where f^{i} is the i - th derivative of the function

If f(x) = e^{-6x}, then the formula of the i - th derivative of the function is:

f^{i} =(-6)^{i} .e^{-6x}----------------------(2)

Then,

f^{i}(0) = (-6)^{i}

Lastly, the equation of the trascendental function by Maclaurin series is: f(x)=\sum_{i=0}^{\infty} \frac{(-6)^{i}.x^{i}  }{i!} \\f(x)=\sum_{i=0}^{\infty} \frac{(-6.x)^{i}  }{i!}---------------(3)

Hence,

The equation of f(x) = e^{-6x} by maclaurin series is f(x)=\sum_{i=0}^{\infty} \frac{(-6.x)^{i}  }{i!}.

Find out more information about maclaurin series here

brainly.com/question/24179531

#SPJ4

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