Can you answer this calculus question?

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.

Answer 1

Sun,

       This is an easy one….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