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Integral Calculus
Using Lagranges multiplier method , find the extreme point of
z=xy , subject to x+y=1 .
z=xy , subject to x+y=1 .
Integral Calculus
Find the second Taylor polynomial of the function , f given by
f(x,y)=e(x+2y) at (-1,1) .
f(x,y)=e(x+2y) at (-1,1) .
Integral Calculus
Find and classify the stationary points of f(x,y)=y2-x2+3xy .
Integral Calculus
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 .
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 .
Integral Calculus
Find dw/dt at t=(pi)/2
where w=x2+y2+2x+3y , x=cos t , y=sin t
where w=x2+y2+2x+3y , x=cos t , y=sin t
Integral Calculus
Compute the jacobian matrices using the chain rule for z=u2+v2 .
where u=2x+7 , v=3x+y+7 .
where u=2x+7 , v=3x+y+7 .
Integral Calculus
derivative of (x+7)^4 =
Integral Calculus
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 .
lim x tends to (pi)/2 (1-sin x)/cos x
if yes , evaluate the limit .
Integral Calculus
Evaluate the limit :
lim x tends to 0+ (ln tan 2x)/(ln tan x) .
lim x tends to 0+ (ln tan 2x)/(ln tan x) .
Integral Calculus
{(x,y) | 0<=y<=3x , 0<=x<=1} is a region of both Type 1 and Type 2 .
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#339914 on Dec 2023
#339914 on Dec 2023