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Can you answer this calculus question?

Let f(x)=sin(x^2)+cos x. 
 
cos (x)=1-(x^2)/2!+(x^4)/4!-(x^6)/6!+...
 
sin(x^2)=x^2-(x^6)/3!+(x^10)/5!-(x^14)/7!+...
 
Use the series for cos (x) and the series for sin(x^2) to write the first four nonzero terms of the Taylor series for f about x=0. 
 
Answer: f(x)=1+(x^2)/2+(x^4)/4!-(121x^6)/6!+...
 
Please show all your work and accurate answer. Thanks.
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1 Answer

Sun,
       This is an easy oneā€¦.just add the first few terms from the series representation for sin(x2) and cos(x) and since they are both even functions you will be able to combine terms with the same exponents. 
jim

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