TEAM PROJECT. Series for Dirichlet and Neumann Problems A) Show that un rncos ne, un = rn sin ne, n = 0, 1, are solutions of Laplace's equation V2u = 0 with V2u given by (5). (What would un be in Cartesian coordinates? Experiment with small n)
B) Dirichlet problem:
Assuming that termwise differentiation is permissible, show that a solution of the Laplace equation in the disk r < R satisfying the boundary condition u(R, 0) = f(e) (R and fgiven) is
u(r) = ao + Σ (an(/rR)n cos ne
where an, b are the Fourier coefficients of f.
C) Dirichlet problem. Solve the Dirichlet problem using (20) if R = 1 and the boundary values are u(e) = -100 volts if -T<< 0, u (8) = 100 volts if 0<

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step-by-step explanation:

∠cbe and ∠deb are same-side interior angles.

i took the test

answer:

given the linear inequality :

add 2y to both sides we get;

simplify:

add 12 to both sides of an equation;

simplify:

divide both sides by 2 we get;

or

the related equation for the inequality equation [1] is;

y-intercepts defined as the graph crosses the y-axis.

substitute x =0 in [2] to solve for y;

y = 6

x-intercepts defined as the graph crosses the x-axis.

substitute value y = 0 to solve for x;

subtract 6 from both sides we get

multiply both sides by 2 we get;

or

x = -12

now, plot these point (0, 6) and (-12, 0) on graph as shown below and shade the graph below the solid line.

8.3 and the 3 is repeating

hope this .