Question

函数题目求

Answer 1

(1)

f(x)
=xsin(1/x) ; x≠0
=0 ; x=0
lim(x->0) xsin(1/x) =0 =f(0)
x=0, f(x) 连续
(2)
y= lntanx
dy/dx
= (1/tanx).(tanx)'
=(secx)^2/tanx
=1/(sinx.cosx)
(3)
x+y= e^(xy)
x=0
0+y= e^(0)
y=1
(0,1)
x+y= e^(xy)
1+dy/dx = ( y+ x.dy/dx) .e^(xy)
[1- xe^(xy) ].dy/dx = y.e^(xy) -1
dy/dx= [y.e^(xy) -1]/[1- xe^(xy) ]
y'|x=0
=dy/dx| (x,y)=(0,1)
= (1 -1)/(1- 0)
=0