Use Fourier transforms to solve the infinite string problem with initial position f(x) and zero initial velocity: [Ytt(x, t) = a2yxx(x, t) — -∞ < x < 00 t> 0 y(x, 0) = f(x) — ∞0 0 t> 0

Q: The domain of the function f(x) = cos-¹(e) is O(-00, 1] O(-∞0,0] O(-∞o, In(cos 1)] ○ [0,00) O[-1,1]

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Q: (b) The Fourier transform of a piecewise smooth function f(x), for which f∞ f(x)|dx exists and is…

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Q: Calculate L{f(t)}

A: A periodic function is a function that assumes the same value after a certain period. A function…

Q: 16 Find the absolute maximum value on (0, ∞) for f(x) = 24 - 4x -

A: Step 1: Step 2: Step 3: Step 4:

Q: (a) A function p(x) with domain (0,8) that has p' (x) > 0 everywhere, p" (x) = 0 for all æ 4. 4 2 4…

A: Given domain of p(x) is 0,8.

Q: 1 Integrate with respect to x. 4+ 25(3x +1)²

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Q: ) If f(x) = (0 <* < 1) (-1 < * < 0) expand f(x) in the form c,P(x).

A: According to our company policy i am supposed to answer ony one question at a time.  For the rest…

Q: The periodic function T(1) obeys T(x+2) = T(x) and |I| 0,n>0 mn= cos(mr) sin(nx)dx □ Σmn Smn²in²n =…

A: Given:  Tx=Tx+2π Tx=1         0≤x&lt;π-1     π≤x&lt;2πIts Fourier transform is given by a0=0,…

Q: A periodic function f(t) is defined as St-1 -1<t<0 f (t)=- t+1 (Ost<1 f (t) = f (1+2) 1) Sketch the…

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Q: (a) State the implicit function theorem in two dimensions. (b) Verify that the equation f(2, 3) = 2²…

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Q: Let f(x) be a function f:[−1,1]→[0,1], f(x)=x^2. Let g(x):(−∞,∞)→[0,1] be a function such that g(x)…

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Q: If the temperature at which a certain compound melts is a random variable with mean value 115°C and…

A: We have to solve given Questions.

Q: (b) Let Y"(t) +2Y'(t) + Y(t) = 3tet, Y(0) = 4, Y'(0) = 2. Then find Y(1). %3D

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Q: (i) (ii) (iii) X, has a pdf f(x₁) = { X₂ has a pdf f₂(x₂) =< x₂ 16 0 x₂²e-x₂²/2 4 0 X, and X₂ are…

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Q: 2 f(x) = tan √√3 10 is a decreasing alues of 2 2x+1 -log (x² + x + 1) + √3 function for all x = R,…

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Q: 1. Draw the graph of a function f which satisfies all of the given conditions. f is continuous on…

A: Here is the solution of the given problem.

Q: Is ƒ continuous at x = -1?

A: From the graph, we see that x=-1 is an endpoint  And it has a closed circle. That means the function…

Q: (b) Let f:(R\{1}) → (R\{1}) and ƒ˜¹:(R\{1} ) → (R \{1}) be both defined by f(x) = f¯¹(x) = = x+1…

A: As both function and its inverse are given in the question so we have to determine that…

Q: T « A-Z O F(x) = -2x² - 5x 08-²+2x² OPx)=x² + 2x³ OF(x)=x²-2x Of(x)=2x²³ - 3x +3 0-³²- Ox)=³-2x³²+x…

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Q: The graph of f(x)= x2 -1 is concave up on interval (-1,1)^O (0,1) 0 (-1,0) U (1, 0 )co…

A: Given,  The function fx = xx2-1  We have to find the interval in which the graph of  fx = xx2-1 is…

Q: Let f(x) = g(x) (x - 1)(x - 2)(x – 3)°(x – 4)³, where g(x) = x + bx² + cx + d. If f(x) is…

A: Use the following formulae, to obtain the required result. duv=udv+vdudu+v=du+dvddxxn=nxn-1

Q: Consider the IVP S2(t) = -1+cos(t + x(t)) cos(t + x(t)) x(0) = 0. Show that the ODE is exact and…

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