Using the Convolution Theorem, what is L[h(t)]?

Q: Q15) A complex-val functio is given in the following. f (2) = %3D a) Find real (u (x, y)) and…

A: Here we use definition of existence of limit to check  f(z) is continuous or not.

Q: f= (2xy+ 3x²)ē+ (x² – 2yz + 2y)ē, – (e² + y²)ēz

A: Given

Q: Prove the following Quotient Rule, where f, g are differentiable:

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Q: Letf be a differentiable function over [0, 2]. The values of the constants a and b such that the…

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Q: Consider the functions: ecos ( z ) x g(x) 1+ (tan æ)² and r(r, s) = 8 . pó + In(1 + s). Let h(r, s)…

A: g(x)=ecos(x)x1+tan x2and xr,s=sr5+ln1+s.To Find: Let hr,s=gxr,s then evaluate hs1.2,0.

Q: Differentiate using product and quotient rule. f(t)=( t-t1/2)/t1/3   (note:your previous answers…

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Q: find FCx)= (i)G)", X =0,1.2 .

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Q: Evaluate L{f(t)} for t+1, t20, t1, t#2 t=1 t=2 (a) f(t)=3, -3,

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Q: Definition: Let f : D → Y be a bijection. The inverse function f-1 : Y → D is a function such that…

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Q: 4. Consider the formula A = Vx (p(x) →q(x)) → (Vxp(x) →xq(x)). (a) Show that A is valid. (b) Show…

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Q: a) f(AUB) = f(A) U ƒ(B). b) (i) f(An B) ≤ f(A)n ƒ(B). (ii) Find a function f {1,2} → {a}, and A, B C…

A: a)  We  have  to prove  that  Now,      Thus,  (Proved)[since, b) i) We  have  to show  that Let  be…

Q: . Let f : [0, 1] R be defined by |-1, z = ; >50 f(x) = {0 |<a < }; 1, 21 (a) Show that f € R([0,…

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Q: Let f(x, y) = 6x³ – 3e²y + 9y. 8u? – 2v || Assume that y = 2uv. Consider the composite function 9(u,…

A: We have to fund the value of gv(u=-1,v=1).

Q: 25. Find the harmonic conjugate of u = In|z| and corresponding analytic function f (z) = u + iv.

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Q: Consider the function h : Z xZ → Z× Z defined by h(x, у) 3D (2ху, 7x — Зу). (a) Is h injective? (b)…

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Q: Let F(x, y, z) = (14xyz + 7sin(x))i + 7x²zj + 7x²yk. Find a function f such that F = Vf. f(x, y, z)…

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Q: Given a function f(x,y,z) = 5x² In (7y + 3z). Find the domain of the function. %3D o {(xy,z) |z >…

A: Use logarithms definition to choose the correct answer.

Q: Q.: Find the radius oP- and the interva l Co nvergence of Gnvergen ce (x-2)" Incn+4)

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Q: IB) Find the cnber of curvatee, eguation of the curde of cuuunfure f (x)> Jax of the gmph. of at x=…

A: Consider the given curve as, fx=2x at, x=4 Let y=fx=2x

Q: Write the Linear Approximation to f(x, y) = x(1 + y)-¹ at (a, b) = (8, 1) in the form f(a+h,b+k)…

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Q: the guotient f(xth) f(a) where h is cortont.

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Q: Use the intermediate value theorem to find the value of c such that f(c) = M. c =

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Q: Evaluate F. dr where F(x, y) = x²y² + 2xyj and C is the boundary of the square (clockwise) through…

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Q: Find F(s). F(s) = L{t(et + est 23

A: Solution is uploaded below.

Q: 2. Let g(x) = [x]. Find: 2.a g ¹({0}) 2.b g¹({-1,0,1}) 2.c g ¹({x 10 < x < 1}).

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Q: determine L−1[F].

A: Given:

Q: Consider the functions f: Rx RR and g: R→ RX R given by f(x,y) = x -y andg(x) = (x,x²) Find the…

A: Given function are f:R×R→R and g:R→R×R defined by fx,y=x−y and gx=x,x2. We have to find the formula…

Q: Let = [ " - 1)5(1 – 2° drt a) find the intervals on which f is increasing and on which f is…

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Q: Use the intermediate value theorem to find the value of c such that f(c) = M. f(x) = = x² - x + 1 on…

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