Find the first three non zero terms in the Taylor Series about z=0 of exp(z sin z)

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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

 

[mrmiller1]

See my attached picture for the Taylor series equation. For Taylor series all you have to do is substitue your given value (z_o = 0) into the original function, the second derivative of the function, the third derivative... and multiply that result by (z-z_o)ⁿ/n! and so on until you obtain 3 terms that are not zero.

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

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