lim(x→-7-0)(x+5)*[|x+7|/(x+7)]
= lim(x→-7-0)(x+5)*[(-1)(x+7)|/(x+7)]
= (-1)lim(x→-7-0)(x+5)
= (-1)(-7+5)
= 2,
lim(x→-7+0)(x+5)*[|x+7|/(x+7)]
= lim(x→-7-0)(x+5)*[(x+7)|/(x+7)]
= lim(x→-7-0)(x+5)
= (-7+5)
= -2.不好意思，能解释下绝对值的问题吗？　　函数 |x+7| 看成分段函数　　|x+7| = (-1)(x+7)，x < -7，　　　　 = x+7，x >= -7。求极限时，　　若x→-7-0，|x+7| 取 (-1)(x+7) 来计算；　　若 x→-7+0，|x+7| 取 x+7 来计算。就这么简单。