lim(x,y)趋向于(2,0)时 (1-cos(x^2+y^2)^(1/2))/(x^2+y^2)

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lim(x,y)趋向于(2,0)时 (1-cos(x^2+y^2)^(1/2))/(x^2+y^2)
lim(x,y)趋向于(2,0)时 (1-cos(x^2+y^2)^(1/2))/(x^2+y^2)

lim(x,y)趋向于(2,0)时 (1-cos(x^2+y^2)^(1/2))/(x^2+y^2)
解;lim(x->2,y->0){[1-cos√(x²+y²)]/(x²+y²)}=[1-cos√(2²+0²)]/(2²+0²)
=(1-cos2)/4
=(2sin²1)/4 (应用余弦倍角公式)
=(sin1)/2.