Question

曲线y= x 4 x 2 −1 arctan 1 x 的斜渐近线为______．

Answer 1

∵x→∞时，arctan1x～1x∴limx→∞yx＝limx→∞x4x(x2−1)•1x＝1又由泰勒公式，得arctan1x＝1x+o(1x3)，从而x4x2−1arctan1x＝(x2+1)[1x+o(1x3)]+1x2−1[1x+O(1x3)]＝x+1x+o(1x3)(x→∞)，limx→∞(y−x)＝0故y=x...