Question

lim(x趋近于0)[sin6x+xf(x)]/x^3=0,则lim(x趋近于0)[6+f(x)]/x^2=?

Answer 1

简单计算一下即可，答案如图所示

Answer 2

lim
x→0,[sin6x
+
xf(x)]/x³=0+α，其中lim
x→0,α=0
即f(x)/x²
=
-sin6x/x³
+
α
从而lim
x→0,[6+f(x)]/x²
=lim
x→0,(
6/x²
-
sin6x/x³
+
α
)
=lim
x→0,(6x-sin6x)/x³，用洛必达法则
=lim
x→0,[6(1-cos6x)]/3x²，用等价无穷小lim
x→0,(1-cosx)等价于lim
x→0,x²/2
=lim
x→0,[
6
×
(6x)²
×
1/2
]/3x²
=36