极限 对数求 lim(x→无穷)(-2x^2 * ln(x^2+2/x^2+1))

来源:学生作业帮助网 编辑:六六作业网 时间:2024/11/17 20:41:49
极限对数求lim(x→无穷)(-2x^2*ln(x^2+2/x^2+1))极限对数求lim(x→无穷)(-2x^2*ln(x^2+2/x^2+1))极限对数求lim(x→无穷)(-2x^2*ln(x^

极限 对数求 lim(x→无穷)(-2x^2 * ln(x^2+2/x^2+1))
极限 对数
求 lim(x→无穷)(-2x^2 * ln(x^2+2/x^2+1))

极限 对数求 lim(x→无穷)(-2x^2 * ln(x^2+2/x^2+1))
x→∞,1/(x^2+1)→0,
——》ln[(x^2+2)/(x^2+1)]=ln[1+1/(x^2+1)]~1/(x^2+1),
——》原式=limx→∞ -2x^2/(x^2+1)
=limx→∞ -2/(1+1/x^2)
=-2/(1+0)
=-2.