Finding the First Three Terms of exp(z sin z) Taylor Series

AI Thread Summary
To find the first three non-zero terms of the Taylor series for exp(z sin z) around z=0, start by calculating the derivatives of the function at z=0. Substitute these derivatives into the Taylor series formula, which involves multiplying each derivative by (z-0)^n/n! for n=0, 1, and 2. The discussion emphasizes the importance of obtaining non-zero results from these calculations. If further assistance is needed after attempting this method, additional help can be provided. Understanding the process of deriving and substituting into the Taylor series is crucial for solving this problem.
blueyellow
find the first three non zero terms in the Taylor Series about z=0 of exp(z sin z)

i have little idea how to even start on the question because it is exp to the power of z sin z and it just looks too complicated. i hav tried looking thru txtbooks for something similar but no similar question exists in the textbooks i hav looked thru so far
can u help please
thanks in advance
 
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See my attached picture for the Taylor series equation. For Taylor series all you have to do is substitue your given value (zo = 0) into the original function, the second derivative of the function, the third derivative... and multiply that result by (z-zo)n/n! and so on until you obtain 3 terms that are not zero.

z - independent variable
zo - your given value of 0
n - the order of derivative taken

Try this and then let me know if you need more help.
 

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