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These are questions asked by Markiyan Hirnyk

The Maple command

int(exp(-z^2*sin(z)^2), z = 0 .. infinity, numeric, epsilon = 0.1e-1);outputs 2.835068335

However, I am not sure if the answer is correct.

Let A and B be matrices of dimensions 3,2 and 2,3 corresondingly. It isknown Multiply(A,B)=Matrix([[8, 2, -2], [2, 5, 4], [-2, 4, 5]])

What is Multiply(B,A)?

limit(t*(int(exp(-t*tan(x)), x = 0 .. (1/2)*Pi)), t = infinity)?

Is it possible to find it in Maple? The command

MultiSeries:-limit(t*(int(exp(-t*tan(x)), x = 0 .. (1/2)*Pi)), t = infinity);outputs.

Is it possible to solve (numerically or symbolically) the system of PDEssys:={diff(Y(x, t), x$2) = exp(-2*x*b)*(A(x, t)-Y(x, t)), diff(A(x, t), t) = exp(-2*x*b)*(Y(x, t)-A(x, t)) }under the conditionsibc:={A(x, 0) = 0, Y(0, t) = 0.1, D[1](Y)(0, t) = 0}, where the parameter b takes the values 0,0.05,0.1, in Maple? The ranges are t=0..7, x=0..20.

The equation

x^7+14*x^4+35*x^3+14*x^2+7*x+88 = 0

has the unique real root

x = (1+sqrt(2))^(1/7)+(1-sqrt(2))^(1/7)-(3+2*sqrt(2))^(1/7)-(3-2*sqrt(2))^(1/7).

Here is its verification:

Is it possible to find that in Maple? I unsuccessfully tried the solve command with the explicit option.

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