Question

高数求极限…大神呀

高数求极限…大神呀13 15 17 小题

Answer 1

如图

Answer 2

(13)
x->0
e^x ~ 1+x +(1/2)x^2
e^x -1-x ~ (1/2)x^2
lim(x->0) [ 1/x -1/(e^x -1) ]
=lim(x->0) (e^x -1 -x )/[x.(e^x -1) ]
=lim(x->0) (1/2)x^2/x^2
=1/2
-------------
(15)
lim(x->0) ln(1+2x^2)/[x.sinx]
=lim(x->0) 2x^2/x^2
=2
-----------------
(17)
lim(x->0) [ √(1-x) - 1 ]/sin3x
=lim(x->0) -x/{[ √(1-x) + 1 ].sin3x }
=(1/2) lim(x->0) -x/sin3x
=(1/2)(-1/3)
=-1/6