Use the Laplace transform to find y(x,s) = 2(c(x,f)) where 8?c(x,t) 1 ac(x,) 0, * > 0, t> 0; k c(x,0) 0, ac(0,1) A, lim, c(x,t) = 0, t> 0. Here, A is a constant; note (or prove) that £(A) = A/s.

Q: (b) x' + 2y' + x = 0, x' − y' + y = 0, x(0) = 0, y(0) = 0 -

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Q: Find the Laplace transform of f(t) t sin(2t) dr F(s) =

A: We use the table of Laplace transform to solve the given question.

Q: 1. Show that the Laplace transform of f is F(s) = r- Fi(s). Hint: Split the domain [0, 0] as [0, T]U…

A: Note: As per bartleby instruction when more then one question is given only one has to be answered.…

Q: 5) f(t)= 2te' 2 Ans. F(s) =- (s –1)

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Q: Find of z = In(xy)

A: Given,Z=ln(xy)differentiating both the sides partially w.r.t. x∂z∂x=1xyy1∂z∂x=1xagain differntiating…

Q: 1) x(t) = 1(t- 47T)

A: Solution 1: Given function is x(t)=1(t-4T)           (1) Let the z-transform of x(t) is X(z)…

Q: 3) x(t) te-at 1 4) x(s) = (Sta)2

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Q: Q. (a) Find an equation of the tangent plane to each surface at the given point. (b) Find symmetric…

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Q: Find the Laplace transform F(s) = L{f(t)} of the function f(t) = (1 – t)(h(t – 1) – h(t – 3)), for s…

A: Rewrite the given function as follows.…

Q: Find the Laplace Transform of function g(t) = {0,    for 0 ≤ t < π…

A: The Laplace transformation of any function  f(t)  is denoted by L[f(t)]   is given by…

Q: Suppose that f: R² → R² is given by f(x, y) = (x³ - 2xy², x+y). Does f has a differentiable local…

A: Inverse mapping theorem.

Q: Q1) Laplace transform of function f(t) = t² where t 2 0 is ....... a) b)금 d) 115 11 1

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Q: Compute the derivative for r(t) = d dt f(t) = (Use symbolic notation and fractions where needed.)…

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Q: Find the derivative of the dot product (u(t) • v(t)) if u(t) and v(t) equal the following (see image…

A: Given vectors are we are to find the derivative of u(t).v(t)

Q: Let (img) Use the fundamental calculus theorem to determine the slope of the tangent line to the…

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Q: (t², 0st<2 Find the Laplace transform of F(t) - 5, t2 2

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Q: 2) Sketch the graph of the following s functions and find the Laplace transfo a) f1(t) = }4 – t, (o,…

A: Given,      (a)    f1(t)=t0≤t&lt;24-t2≤t&lt;40t≥4      (b)    f2(t)=00≤t&lt;1t1≤t&lt;21t≥2

Q: Show the following functions are holomorphic on the domains given, and compute their derivative…

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Q: Find the Laplace transform F(s)=L{f(t)}F(s)=L{f(t)} of the function f(t)=6+sin(3t)f(t)=6+sin(3t),…

A: From the given statement, the function is f(t) = 6+ sin(3t).

Q: A rental truck costs $45.45 for a day plus 94¢ per mile. (a) If x is the number of miles driven,…

A: Given that, a rental truck costs $45.45 for a day plus 94c per mile.

Q: Find the Laplace transform for 1 (a) f(t) = sin? t J 3) (b) f(t) = e-4t sin 3t (c) f(t) = t sinh 5t

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Q: The inverse Laplace transform of the function F(s) = = a) y(t) = 2 cost + 3 sint b) y(t) = 2e' cost…

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Q: Use the definition of Laplace Transform, F(s)=∫∞0e-sx*f(s)dx to show that L{f'(x)}=s*F(s)-f(0).

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