Rolle's Theorem on the

Q: 1. cosh z= cosh x cos y + i sinh sin y sinh z = sinh x cos y + i cosh x sin y.

A: According to our guidelines we are supposed to answer only one question, since you have asked more…

Q: Jc 1-2² CK 1+2 cose de. 5+4 cos 8 3. Using contour integration evaluate f

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Q: Lagrange's Theorem If a function f(x) is continuous in the closed interval [a, b] and is…

A: Proof of Lagrange's theorem.

Q: F(x)= [² cos(y) 1+ y² dy

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Q: 1 = (3, -2, f(t)= -0.1+ ≤ t ≤ 0.1- 0.1+ ≤ t ≤ 0.4

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Q: B-Test and proof the function So (x In x)² dx

A: ∫01(x logx)2dx=∫01x2 (log x)2dx use integral by parts, ∫udv=uv-∫vdu u=(logx)2…

Q: Property 5. If X is some r.v. with characteristic function ox (t), and if u,' = E (X) exists, then…

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Q: laplace of a2u2(a)

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Q: Bessel's Function 1. Find Jg cx ) (x)

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Q: 2 inverse laplace 5 Examples

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Q: 3) Prove thet the xy-plane with constant curva tue k= urve In is o circle of radious

A: We have to prove that a curve in the xy plane with constant curvature k=1r is a circle of radius r

Q: 5. L (s 2 s +2 + 4s+ 5)² e 6s

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Q: 5) f(t) = f(t) = e¯2t/1+ sin2t

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Q: e cosl – i e™ sin 1 + e¯ cos 1 - i e- sin 1 2 e cosl + i e™ sin 1 – e- cos 1 + i e¯I sin 1 -TT 2 e…

A: Simplify the given expression: Coshπ-i

Q: Actual question: • State any form of Green's theorem; • Under what conditions does Green's theorem…

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Q: laplace of a2u4(a)

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Q: * Let A E R"Xn, ĩ E R" \ {0} and A = 0. Prove that if the origin is stable if and only if ī is…

A: Given A∈ℝn×n,x¯∈ℝn\0 and Ax¯=0 To prove that the origin is stable if and only if x¯ is stable.  If…

Q: The joint pdf for A₁ and A2 is for 1 1, 2, 3 and 22 = 1, 2, 3. = (a) Find the pdf of Y = (b) Find…

A: (a) To find the probability density function (pdf) of Y = X1 X2, we first need to find the range of…

Q: 6. (sin' 20 cos' @ dө 8. (sin? x сos' x dx

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Q: Degree of Field Extension [Q(i),Q]

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Q: Use logarithmic differentiation to find the derivative of each function. 1) y=Vxe" (x* +1)"

A: According to our guidelines we are supposed to answer only one question since you have asked more…

Q: Using Cenveludion that' theorem prave convo let=sınt-cost) (6+) (S*1)_{

A: Let F(s) and G(s) be two functions.  The convolution theorem states that L-1FsGs=∫0tfugt-udu, where…

Q: 1.333 points Save Answer 3z -2 Let f (z)=- How many poles of order 2 has the function f? (z-27(z…

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Q: Bessel's Function Tutorial sheet J, (x) Find ý and ý 2. y =

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Q: How do

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Q: y" + ay '- 3y sin 2x y o) =y'0) =12

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Q: If (-3, 1) is in the function f(x), then which of the following points will be in the function f…

A: (-3, 1) is in f(x)  Hence,  f(-3)  =  1    Taking the inverse of f at both sides    f-1 ( f(-3) )  =…

Q: n-1 Show that : [(n) = Ln dx ,n > 0 %3D 1 Show that if n> 0, m =,(n – 2) , then : 2m + 2 3* r (n +3)…

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Q: Let f. q, and h be the functions defined on R by if – 1 4, and h(r) = e-2. Consider the following…

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Q: 19 5-2 3s+5 + н 85

A: To find the inverse Laplace transform.

Q: Suppose f(1) = 2, ƒ'(1) = 3, ƒ (2) = 1, ƒ'(2) = 4, and g(1) = 3,g'(1) = 5,g(2) = 1,g′(2) = 4. If…

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Q: af af Әх' ду f(x, y) = 3(x2 + y2) log(x2 + y2), (x, y) ≠ (0, 0) 3x(log(x2 + y2) + 1) Find Əf ах af…

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Q: (i) If y =g (x1- x2). Let u = x1- x2, show that (a) ay/du = ây/Əxı=- dy/ax2 %3D (b) a@y/ðu² = y/Əx¡²…

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Q: laplace transform L { cos(2t) }   pls use integration by parts

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Q: Finden- un) andrn - in twe dferent mays r(t) -n+ se's - e'N, wt) - t'k (a) re) - uch) () Find the…

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Q: QI] (A) If F(x+y-z.x² + y°)= 0_where := z(x, y) and+ 0 then prove x- =x-y

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