) The Laplace trancform Of the function f(t) exists if: Ai f(t) is at least piecenise or sectionally Won tinuous in. every finite interval t7 or B, f(t) is of exporential order to zero- %3D C. Both and D. Neither A nor

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A: Given: z=ln(x2+y2)+2 tan-1(yx)

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Q: Show that each function in Exercise satisfies a Laplaceequation.ƒ(x, y) = e^-2ycos 2x

A: Given :

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Q: Find the divergence at Iol g0o o) for Hure Vcetor Ficuld F (Xoyaz) =e*sínyi-c" ă cos yjt z°k

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Q: 1) Given the vector-valued function r(t]=e",-te"",tlnt) Evaluate lim r(t) and Evaluate lim r(t) b-…

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A: The given problem is to find the Laplace transform of the given function using integral method.

Q: 9. Consider the equation d?x + q(t)x = 0, (A) di? where q is continuous on a stsb and such that 0 <…

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Q: T 2 If fo)= J* +?dt, use the fundemental theorem of culculus part 1, to find f'cx) fixs=

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Q: Consider the function f defined on [0, 1] such that f(0) = 1, f(1) = 3, f(1/5) = f(3/5) = 4, and…

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Q: Show that the following function satisfies the two-dimensional Laplace's equation. z = In(x² + y²) +…

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Q: Suppose that Di is the open disk with center 0 and radius 1. Let f(z) be analytic on Di \ {0} and…

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Q: F(X)=JX F: [o,2]-> show i fis lipschit z funcla or not find k to

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Q: f(x, y) =(e-2y)Cos2x

A: The Laplace equation is: ∂2f∂x2+∂2f∂y2=0

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A: On some rearrangement you will get,

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Q: HW.8. Use farseval's theorem to find if f(t)=A e-alti Ans: A?

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Q: Q2. If ƒ = In(x² + y² +Z? ) then find the divergence of f also find its magnitude at (1,-2,3).

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Q: 7. let E be the reyion bounded by curve 2+2 in the yex? fint quadant let u xy, Vzy-x d Czry)…

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Q: Consider the function f defined on [0, 1] such that f(0) – 1,f(1) = 2,f0/5) = f(2/5) 3. and f()-cand…

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Q: B. Use Green's theorem to evaluate f (x²y)dx + y²dy Where C is close path formed y = x and y = x³…

A: Above first question is solved. Solving more than one question is against the policy of bartleby.

Q: (a) If A = (4xy – 3x²2²)i + 2x?j – 2x°z k, prove that A dr is independent of the curve C joining two…

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Q: Let f (z)=z. Find zpl 2) from z =0 to z =4+2/ alongthe curve C given z 21 to z =2i.

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Q: Q2 :- IS fixg)= e then O PYoue that fcag) Continuons d (o,0) that fay =S,x O shaw wether if feay)…

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Q: If f(z) = u + iv is entire and u(x, y) is bounded above, apply Liouville's Theorem to exp(f(z)) to…

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Q: Solve the problem with Neumann oundary conditions, - Uxx = 0, x, t > 0 u(x, 0) = f(x) ux (0, t) = 0…

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Q: Consider the function f defined on [0, 1] such thatf (0) = f(1) = 1,f(1/5) = f(3/5) 2, and f (2/5) =…

A: Solution:

Q: If f:[a, b] →R has a local minimum at p E (a, b) and f is differentiable at p, then prove that f'(p)…

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Q: Given the interval [a,b] that saitisFies the hypothesis of Rolle's Theorem For the Furnction f(x) =…

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Q: Vt-2 lim (vt – 3, (;) tan t→4 t-4

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Q: Show that the subtangent to y = x' at x = a is equal to a/3.

A: Definition used -                            Length of subtangent =ydxdy

Q: *6. Let f: R' →R be given by =+4x'z-6xyz+4y-3x'y. Is M=f-((0}) a smooth surface (2-dimensional…

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Q: Without using the shift formula prove that Laplace of f (t) = e**-atcos wt is w**2/((s+a)**2+w**2)

A: