( 1)。 It is known that x → 0lim [(x-arctanx)/x k] = c, where k and c are constants and c≠0, then k=? c=？

Solution: x → 0 lim [(x-arctanx)/x k] = x → 0 lim [1-1(1+x? )]/[kx^(k- 1)]=x→0lim(x？ )/[k( 1+x？ )x^(k- 1)]

=x→0lim{ 1/[k( 1+x？ ) x (k-3)] = c, so k=3 and c= 1/3. Choose D.

(2)。 Find the surface x? The tangent plane equation of +cos(xy)+yz+x=0 at point m (0, 1,-1)

Solution: Let F(x, y, z)=x? +cos(xy)+yz+x=0

F/？ X=2x-ysin(xy)+ 1, at point m,? F/？ x∣(0, 1,- 1)= 1；

F/？ Y=-xsin(xy)+z, at point m,? F/？ y∣(0, 1,- 1)=- 1；

F/？ Z=y, at point m,? F/？ z∣(0, 1,- 1)= 1；

Therefore, the cross-sectional equation of m is x-(y- 1)+(z+ 1)=0, that is, x-y+z+2=0 is the demand. Choose one.