Solve the heat flow problem shown below with ß= 3, L=x, and the given function f(x)=2 sin (x) - sin (2x) du au at (x, t)=B 2(x, t), 00, u(0, t)= u(L, t)=0, t>0, u(x, 0)=f(x), 0

Q: 4. The two differentiable functions f(r, g) and g(r,0) satisfy the identity 9(r, 6) = S(r cose, r…

A: Given two differentiable function are f(x,y) and g(r,θ)  such that g(r,θ)=f(rcosθ,rsinθ) given that…

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A: given x=cos2t and y=cost interval 0&lt;t&lt;π  dx/dt =d/dt(cos2t) dx/dt=-2sin2t And dy/dt=d/dt(cost)…

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A: Since, we have been given that r(z)= sin(z2-10z+16)Our Aim is to find r'(z)=?

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A: We can apply fundamental theorem of calculus here.  The second fundamental theorem of calculus…

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A: According to the question,

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A: Solution

Q: Let f(x) = Then f'(x) = π The equation of the tangent line to y = f(x) at a = can be written in the…

A:

Q: yes, hi. I've seen another source, use set variables to 0 and then solve individually, answers are…

A: setting z=0 and solving for x and y. similarly setting y=0 and solving for x and z.

Q: If f(x, y) = ln(x + y), then total derivative or total differential of f at x = 3 and y = 20 is : Y

A: Given data: The given expression for the function is f(x,y)=ln(x+y). The given value of x is x=3.…

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A:

Q: Find f. f"(x) = 5e* – 8 sin(x), f(0) = 3, = 0 %3D %3D f(x) = IN

A: Answer and explanation is given below

Q: Verify that the function u=e(-α^2)t sin x is a solution of the heat conduction equation ut = α2uxx

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Q: Find f. f "(t) = 5e + 8 sin t, f(0) = 0, f(x) = 0 f(t) :

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Q: - Differentiate the function (find F'(x)) if F(x) = sin(t² + 1) dt

A: Apply Leibnize's. Rule

Q: 5. Let F(x) : = a sin(3.x) + bx cos(3x). Find constants a, b such that F'(x) = 2x sin(3x) and verify…

A: The detailed solution is given below Thank you

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A: The given function is  and the direction  at .The aim is to find the derivative .

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A: Given: vxx+vyy=xy   …1, x∈0,π, y∈0,πv0,y=0vπ,y=sin2yvx,0=sin3xvx,π=0 We have to solve equation (1).…

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A: Given, fx and gx be differentiable functions such thatf3=1f0=2f'3=2g1=0g'1=2 Used differentiation…

Q: 2. Solve for y in the equation y = e* sin x + e* cos x – y +c 3. Solve for f e* sin x dx in the…

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Q: 12. Find frxyz for f (x, y, z) = sin (3x + yz)

A:

Q: If f(x) = 4 sin(x) + In(3x), find f'(x). f'(x) = Graph f and f' in the same viewing window. y y 4 2…

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Q: Given f(x, y) = 4e2" sin(2y) %3D then V f(0, 7) =

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Q: 8. Integrate, cos(x) – 1 s X dx

A: Now solving:This is a special integral (Cosine integral):=Ci(x)Now solving:This is a standard…