In Mathematica, how can I cut off the high-order terms in a polynomial?

wolfram-mathematica

Solution

In[1]:= y = a0 + a1*x + a2*x^2 + a3*x^3 + a4*x^4;
y /. x^b_ /; b >= 3 -> 0

Out[2]= a0 + a1 x + a2 x^2

Problem

For example, I have a polynomial y＝a_0＋a_1 x + ..... + a_50 x^50. Since I know that the high-order terms are imposing negligible effects on the evaluation of y, I want to cut off them and have something like y＝a_0＋a_1 x + ..... + a_10 x^10, the first eleven terms. How can I realize this? I thank you all in advance.

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