一道简单的高数题,若x趋近于0时,[sin(6x)+xf(x)] / (x^3)的极限为0,则x趋近于0时,[6+f(x)] / _数学解答

一道简单的高数题,
若x趋近于0时,[sin(6x)+xf(x)] / (x^3)的极限为0,则x趋近于0时,[6+f(x)] / (x^2)的极限为：
A、0
B、6
C、36
D、无穷

人气：148 ℃　时间：2020-10-01 19:01:35

解答

lim [6+f(x)] / (x^2) = lim x[6+f(x)] / (x^3)
=lim (6x+xf(x))/x^3
=lim (6x -sin(6x) + sin6x + xf(x))/x^3
=lim (6x -sin(6x))/x^3+ lim [sin(6x)+xf(x)] / (x^3)
=lim (6x -sin(6x))/x^3+0
=lim (6(1-cos(6x)))/(3x^2)用洛毕塔
=36