Calculus Answers

If f(x,y)=x^2tan^-1(y/x)y^2tan^-1(x/y)[xnot=0,y not=0]
=0(x=0=y)
then show that
(Partial d^2f)/(partial dx *partial day)=(x^2-y^2)/(x^2+y^2)

Evaluate the integral by converting to polar coordinates

INTEGRAL SIGN(0to √3) INTEGRAL SIGN (y to√(4-y^2))[dxdy/4+x^2+y^2]

If possible then find the value of f such that

F=(4x^3+9x^2y^2,6x^3y+6y^5)=∇f

Find the value of a,b and c such that

lim xtend to infinity(ae^x-bcosx+ce^-x)/xsinx=3/2

Obtain the curl of the following vector field:rA = ( eˆ r + r c o s θ eˆ θ + r eˆ φ )

express the vector field F =zxi^+(x^2+y^2)j^+(x/z)k^in cylinderical polar coordinate.

Show that for two scale field f and g : ∇×(f ∇g)+∇×(g∇f)=0

Find the area enclosed by curve r= a(1-cos theta)

Find the volume of the solid of revolution
obtained by revolving the area under the
3 curve y = 2 + x^3
between x = 0 and x = 2
about the x-axis. Draw a rough sketch.

Find the length of the curve given by x = t^3,
y = 2t^2 in 0<= t/<=1. What is the slope of the
curve at t = 1/2 ?