I needed to make the first order Taylor series with the function Series. I received a second order term in the result. Mathematica version 11.0.1.0 on Mac.

I think that something is wrong with the function Series[]. I take a simple function as example In[15] and want to obtain Taylor series of the first order on x,y near point (0,0). I received an expression Out[18] which has last term 0.741907xy which is the second order. A right expression Out[19] different from Out[18] can be received by direct calculating Taylor series, In[19]

Clear[f, x, y]
f[x_, y_] = Sin[1 + x + y]/(2 + Cos[2 - x + y])

seri1 = Series[f[x, y], {x, 0, 1}, {y, 0, 1}] // N
seri2 = Expand[Normal[seri1]]
seri3 = N[f[0, 0] + x*(D[f[x, y], x] /. {x -> 0, y -> 0}) + y*(D[f[x, y], y] /. {x -> 0, y -> 0})]