2----- (ai)
f[x_,y_]=x^2*y+y^2*x+x^3+y^3;
D[f[x,y],x]
s+i
D[f[x,y],y]
s+i
D[f[x,y],{x,2}]
s+i
D[f[x,y],{y,2}]
(aii)
f[x_]=Abs[x+1]+Abs[x];
lhs=Limit[f[x],x->-1,Direction->1]
rhs=Limit[f[x],x->-1,Direction->-1]
f[-1]
lhs==rhs==f[-1]
2 (b)
L1=Table[k,{k,1,100}];
L2=Table[7*k,{k,1,100/7}];
L3=Complement[L1,L2];
L4=Partition[L3,5];
TableForm[L4,TableAlignments->Left]
3 (a)
ContourPlot3D[{z==5*x^2+5*y^2,z==6-7*x^2-y^2},{x,-5,5},{y,-5,5},{z,12,6},Axes->T
rue,Boxed->False]
need
3 (b)
a={2i-j+k};
b={-i-3j-5k};
c={3i-4j-4k};
u=Cross[a,b];