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Find the terms through degree 4 of the Maclaurin series.

f(x) = 6eᵉˣ (Express numbers in exact form. Use symbolic notation and fractions where needed.

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Final answer:

The terms through degree 4 of the Maclaurin series for f(x) = 6e^e^x can be found by using the formula for the Maclaurin series expansion of e^x and substituting it into the function.

Step-by-step explanation:

The Maclaurin series for the function f(x) = 6eex can be found by using the formula for the Maclaurin series expansion of ex. The formula is:

ex = 1 + x/1! + x2/2! + x3/3! + x4/4! + ...

By substituting ex into the formula and simplifying, we get:

f(x) = 6(1 + (e^x)/1! + (e^x)^2/2! + (e^x)^3/3! + (e^x)^4/4! + ...)

Now we can calculate the terms through degree 4 of the Maclaurin series:

f(x) = 6(1 + x + x2/2! + x3/3! + x4/4!)

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