Use the definition of a Taylor series to find the first four nonzero terms of the series for f(x)f(x) centered at the given value of aa. (Enter your answers as a comma-separated list.)
f(x)=51+x, a=2f(x)=51+x, a=2
Failure of Taylor's Theorem:
Taylor's Theorem fails to expand f(x+h) in an infinite series in the following situations:
(i). If any functions f(x), f′(x), f′′(x),......f(x), f′(x), f″(x),...... becomes infinite for any value of x in the interval under consideration.
(ii). If Rn=hnn!f(n)(x+θh)Rn=hnn!f(n)(x+θh) does not tends to zero as n→[infinity].
f(x)=