Find First 5 Nonzero Terms of Maclaurin Series for $e^{4x} \sqrt{1+x}$

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SUMMARY

The discussion focuses on finding the first five nonzero terms of the Maclaurin series for the function \( f(x) = e^{4x} \sqrt{1+x} \). Participants suggest deriving the series for \( e^{4x} \) and \( (1+x)^{1/2} \) separately before multiplying the results. This method effectively combines the series to achieve the desired terms for the function. The approach is confirmed as valid and necessary for exam preparation.

PREREQUISITES
  • Understanding of Maclaurin series expansion
  • Familiarity with the exponential function series \( e^{x} \)
  • Knowledge of the binomial series for fractional exponents
  • Basic algebraic manipulation skills
NEXT STEPS
  • Learn how to derive the Maclaurin series for \( e^{4x} \)
  • Study the binomial series expansion for \( (1+x)^{1/2} \)
  • Practice multiplying series to find combined terms
  • Explore applications of Maclaurin series in calculus problems
USEFUL FOR

Students preparing for calculus exams, particularly those focusing on series expansions, as well as educators seeking to clarify Maclaurin series concepts.

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find the first 5 nonzero terms in maclaurin series. (might be binomial)

$f(x)=e^{4x} \sqrt{1+x}$my book doesn't explain it properly and my instructor didnt explain it and I am very stuck and there's going to be one similar to this on the test. help!
 
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ineedhelpnow said:
find the first 5 nonzero terms in maclaurin series. (might be binomial)

$f(x)=e^{4x} \sqrt{1+x}$my book doesn't explain it properly and my instructor didnt explain it and I am very stuck and there's going to be one similar to this on the test. help!

Find a series for $\displaystyle \begin{align*} \mathrm{e}^{4x} \end{align*}$, find a series for $\displaystyle \begin{align*} \left( 1 + x \right) ^{\frac{1}{2}} \end{align*}$ and then multiply them together...
 
ok thanks. nice "seeing" you again Prove It. :)
 

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