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

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To find the first five nonzero terms of the Maclaurin series for the function f(x) = e^{4x} √(1+x), one must first derive the series for e^{4x} and the binomial series for (1+x)^{1/2}. The Maclaurin series for e^{4x} is 1 + 4x + (4x)^2/2 + (4x)^3/6 + (4x)^4/24, while the series for (1+x)^{1/2} is 1 + (1/2)x - (1/8)x^2 + (1/16)x^3 - (5/128)x^4. Multiplying these two series together will yield the desired terms. This approach is essential for solving similar problems on upcoming tests. Understanding these series expansions is crucial for mastering calculus 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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