a)Calculate the area between f(x)=ln(x) curve and x=0, y=0, x=e. Show the area with graphic. b)Calculate the domain off(x,y)= [ (x+y)/(x-y) ]...
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1.a)    Calculate the area between f(x)=ln(x) curve and x=0, y=0, x=e. Show the area with graphic.

b)    Calculate the domain of f(x,y)=√ [ (x+y)/(x-y) ] function as algebraic and geometric.

c)    Show that is zxx+zyy differential equation satisfy  z=tan-1[(2xy)/(x2-y2)]   equation.  

2.

a) Calculate maximum volume of box which in the trihedral coordinate planes and one corner located on the x+y+z=3 plane.

b) an [an}  arithmetic sequence a3=6 and a9=20 calculate the general term of sequence, organize sequence, search is the sequence's convergent or divergent.

c) an an  arithmetic sequence a3=1 and a6=1/8 calculate the general term of sequence, organize sequence, search is the sequence's convergent or divergent.

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