Question

高等数学极限题

问题如图，要有具体过程，谢谢

Answer 1

把x=2带入x-2中得分母为零，若分子不为零，则极限无穷大，所以若想极限不是无穷大，只有分子同时为0，由罗比达法则得到极限等于3，所以把x=2带入分子得a+2=0，解得a=-2

Answer 2

Answer 3

f(x)
=sinkx/√(1-cosx) ; x<0
=(1/x)[lnx-ln(x+x^2)] ; x>0
x->0-
sinkx ~ kx
√(1-cosx) ~ -(√2/2)x
f(0-)
=lim(x->0-) sinkx/√(1-cosx)
=lim(x->0-) kx/√[-(√2/2)x]
=-√2k
f(0+)
=lim(x->0+) (1/x)[lnx-ln(x+x^2)]
=lim(x->0+) (1/x)ln[x/(x+x^2)]
=lim(x->0+) (1/x)ln[1/(1+x)]
=lim(x->0+) (1/x)[-ln(1+x)]
=lim(x->0+) (1/x)(-x)
=-1
f(0+) =f(0-)
-√2k=-1
k =√2/2

Answer 4

C