A calculus problem by Guillermo Templado
Which is the first term in Taylor's serie of f(x)=tg (x)cos (x) around x=0?
The answer is 0.
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1 solution
While you didn't state that the first term would be x
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You mean the first term different of 0. In a Taylor's serie of f(x) around x=0 , the first term (in the sum) is f(0)/0!, the second term is f'(0) x/1!, ...
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The taylor series would be:
x − 3 ! x 3 + 5 ! x 5 − . . .
Hence the first term is x and around x = 0 , the value is 0.
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@Gian Sanjaya – The taylor serie of f(x)=tg(x)cos(x)=sen (x) ( although,we have to state the domain of the function..) around x=0 would be: 0 + x +(0/2!)x^2 - x^3/3!+...
the first term in Taylor's serie of f(x) around x=0, is f(0). In this case, f(0)=0