Solve the following initial/boundary value problem:
∂u(t,x)/∂t = ∂^2u(t,x)/∂x^2 for t>0, 0<x<π,
u(t,0)=u(t,π)=0 for t>0,
u(0,x)=sin^2x...
Solve the following initial/boundary value problem:
∂u(t,x)/∂t = ∂^2u(t,x)/∂x^2 for t>0, 0<x<π,
u(t,0)=u(t,π)=0 for t>0,
u(0,x)=sin^2x for 0≤x≤ π.
if you like, you can use/cite the solution of Fourier sine
series of sin^2(x) on [0,pi] = 1/4-(1/4)cos(2x)
please show all steps and work clearly so I can follow your
logic and learn to solve similar ones myself.
Please show complete, step by step
working.
Solve the following equations for 0 ≤ x ≤...
Please show complete, step by step
working.
Solve the following equations for 0 ≤ x ≤ 2π, giving
your answers in terms of π where appropriate
i) cos
x = -√3/2
ii) 2 sin
2x = 1
iii) cot x =
1/√3
b) Solve the following for 0° ≤ q ≤
360°,
i) sin^2Q = 3/4
ii) 2 sin^2Q - sinQ = 0 {Hint: factor out sinθ)
Evaluate ∮C(x^3+xy)dx+(cos(y)+x2)dy∮C(x^3+xy)dx+(cos(y)+x^2)dy
where C is the positively oriented boundary of the region bounded
by C:0≤x^2+y^2≤16, x≥0,y≥0C:0≤x^2+y^2≤16,x≥0,y≥0
Evaluate ∮C(x^3+xy)dx+(cos(y)+x2)dy∮C(x^3+xy)dx+(cos(y)+x^2)dy
where C is the positively oriented boundary of the region bounded
by C:0≤x^2+y^2≤16, x≥0,y≥0C:0≤x^2+y^2≤16,x≥0,y≥0
Find the value of C > 0 such that the function
?C sin2x, if0≤x≤π,
f(x) =...
Find the value of C > 0 such that the function
?C sin2x, if0≤x≤π,
f(x) =
0, otherwise
is a probability density function.
Hint: Remember that sin2 x = 12 (1 − cos 2x).
2. Suppose that a continuous random variable X has probability
density function given by the above f(x), where C > 0 is the
value you computed in the previous exercise. Compute E(X).
Hint: Use integration by parts!
3. Compute E(cos(X)).
Hint: Use integration by substitution!
X =
{a,b,c,d,e}
T = {X, 0 , {a}, {a,b}, {a,e}, {a,b,e}, {a,c,d},
{a,b,c,d}}
Show that...
X =
{a,b,c,d,e}
T = {X, 0 , {a}, {a,b}, {a,e}, {a,b,e}, {a,c,d},
{a,b,c,d}}
Show that the sequence a,c,a,c, ,,,,,,, converges to d.
please...