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Using the method of separation of variables, solve uxt=e^-t cos x when u(x,0)=0, ∂u/∂t (0,t)=0
solve; [D^3 − DD′^2 − D^2 + DD′] z = 0
Evaluate: lim x→infinity(√2x^2+3x-2 -√2x^2-3x+2)
Find the slope of the tangent at (3,1,1)to the curve of intersection of x=3 and z= x^2y-3xy^2+1.
Evaluate: lim x→∞ [(√ 2x^2 +3x- 2)-(√ 2x^2-3x+2)]
Apply Inverse function theorem to check the local invertibility of the following
function f: R^2 → R^2 given by at the point (0, π).
f(x,y)=(y cosx, x-y+2)
function f: R^2 → R^2 given by at the point (0, π).
f(x,y)=(y cosx, x-y+2)
Find the directional derivate of
f(x,y)={2xy/(x^2+y^2), (x,y)≠(0,0) ; 0, (x,y)=(0,0)
at (0,0) in the direction of (i) θ=π/2, (ii) θ=π/4
f(x,y)={2xy/(x^2+y^2), (x,y)≠(0,0) ; 0, (x,y)=(0,0)
at (0,0) in the direction of (i) θ=π/2, (ii) θ=π/4
If , z = e^x sin y where x = st^2 and y = s^2 t, find ∂z/∂s and ∂z/∂t
.
.
Find the moment of inertia I2 for the solid above the xy-plane bounded by the
paraboloid z = x^2 + y^2 and the cylinder , x^2 + y^2 = 9 assuming the mean density to
be constant C.
paraboloid z = x^2 + y^2 and the cylinder , x^2 + y^2 = 9 assuming the mean density to
be constant C.
Prove that the functions g(x, y)= (2x-3y)/(4x+5y) and h(x,y)=x/y, y≠0, y≠-(4/5)x are functionally dependent.
