Yes you can.
Taylor polynomial about x = 0 called Maclaurin polynomial.
Maclaurin polynomial for sin x is:
sin x = x / 1! - x³ / 3! + x⁵ / 5! - x⁷ / 7! ...
so
x sin x = x ( x / 1! - x³ / 3! + x⁵ / 5! - x⁷ / 7! ... ...)
x sin x = x² / 1! - x⁴ / 3! + x⁶ / 5! - x⁸ / 7! ...
The fourth degree Taylor (in this case Maclaurin) polynomial of x sin x about x = 0:
x sin x ≈ x² / 1! - x⁴ / 3!
x sin x ≈ x² - x⁴ / 6
One more question...
If you have f(x) = xsinx and the question is asking for the fourth degree Taylor polynomial about x=0, can you use the sinx Taylor polynomial series equation? I'm confused because there's the x in front so I don't know how to incorporate that part.
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