Integral Calculus Answers

Evaluate fxy at a point (x,y) for the function f defined by f(x,y)=x (1/tan) y .
Using Schwarz's Theorem evaluate fyx at the point (x,y) .

Show that the functions f(x,y)= y/x and g(x,y)= (x-y)/(x+y) are functionally dependent .
Find a functional relation between them .

Using Lagranges multiplier method , find the extreme point of
z=xy , subject to x+y=1 .

Find the second Taylor polynomial of the function , f given by
f(x,y)=e(x+2y) at (-1,1) .

Find and classify the stationary points of f(x,y)=y2-x2+3xy .

Show that the open sphere S with centre at (3,1,4) and radius 5 in R3 is contained in the open cube
P1={(x,y,z) : |x-3|<5 , |y-1|<5 , |z-4|<5} and P1 is contained in the sphere with centre (3,1,4) and radius 8.66 .

Find dw/dt at t=(pi)/2
where w=x2+y2+2x+3y , x=cos t , y=sin t

Compute the jacobian matrices using the chain rule for z=u2+v2 .
where u=2x+7 , v=3x+y+7 .

derivative of (x+7)^4 =

Can L' Hospital's rule the applied to evaluate the limit
lim x tends to (pi)/2 (1-sin x)/cos x
if yes , evaluate the limit .