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Find the nth Taylor polynomial for the function, centered at c. f(x) = x^cos x, n=2, c=s Step 1 Iff has nth derivatives at c, then P(x) = f(c) + f(c)(x-c)+(c)(x-c)²+(c)(x-c)³. 21 is called the nth Taylor polynomial for fat c. Find the following derivatives, which we need to find the polynomial. f(x)=x² cos x F00-4x cos(x)-xsin(x) 7") - 12x cos(x)-8x³sin(x)-xcos(x) Step 2 Evaluate each derivative at F(x)=x^cos x F(x) 4x² cosx-xsin x phi 12 con t 31 K(4) cos(s)-in () XXX) - Cosp He -4 f"(c)(x-c)" n 12³ con (a)-com (2) Aralin (2) -4² -12²+

Step 3 Substitute the values of the derivatives obtained, in the previous step in the second degree Taylor polynomial and simplify F"(x)(x-x) -P₂(x) = f(a) + F(x)(x- P₂(x)== + Submit 2 4 Skip (you cannot come back) 1x-