The Taylor series for f(x) = x3 at -1 is cn(x+1)n. Find the first few coefficien

Question

The Taylor series for f(x) = x3 at -1 is cn(x+1)n. Find the first few coefficients. Box 1: Enter your answer as a number (like 5,-3,2.2) or as a calculation (like 5/3,2 3,5 + 4) Enter DNE for Does Not Exist, oo for Infinity Box 2: Enter your answer as a number (like 5,-3,2.2) or as a calculation (like 5/3,2 3,5 + 4) Enter DNE for Does Not Exist, oo for Infinity Box 3: Enter your answer as a number (like 5,-3,2.2) or as a calculation (like 5/3,2 3,5 + 4) Enter DNE for Does Not Exist, oo for Infinity Box 4: Enter your answer as a number (like 5,-3,2.2) or as a calculation (like 5/3,2 3,5 + 4) Enter DNE for Does Not Exist, oo for Infinity Box 5: Enter your answer as a number (like 5,-3,2.2) or as a calculation (like 5/3,2 3,5 + 4) Enter DNE for Does Not Exist, oo for Infinity).

Explanation / Answer

f(-1) = -1

f'(x) = 3x2; f'(-1) = 3

f''(x) = 6x; f'' (-1) = -6

f'''(x) = 6; f''' (-1) = 6

f(4) (x) = 0

This gives

c0 = -1

c1 = 3/1! = 3

c2 = -6/2! = -3

c3 = 6/3! = 1

c4 = 0

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