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Q: Q2: Iff (z) is analytic at zo. (b) Give an example to show that the converse of (a) is not…

A: If f(z)  is analytic at Z0  Then it must be continuous at Z0  We already prove.  Now we consider…

Q: 3. Find and sketch the domain of f(x, y) = In(9 – x² – 9y²). [Hint: In(x), x > 0]

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Q: Q2/ fincd lachre trans form for at X- 3x+2X=lee

A: given equationx"-3x'+2x=1-e2tby assuming that initial condition is zero.x"=s2X(s)and x'=sX(s)and…

Q: Find the Sclutian to the an=2anal t3an-2 with terms lecurrence relation initial and

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Q: find the funotion with hejp of a indegral meau value betw een 4,1] of g(x)=\xl-2

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Q: Give the condition which ensure that Je-| < 1 where z E C.

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Q: by f(x) = (x2 + 1)35 for all x e Ris A. One-One but not onto B. onto but not one-one C. neither…

A: Given f(x) = (x2 + 1)35

Q: Find the meteix A of the Lineak teansfoRmati on foom IRto IR . 2. given by x2

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Q: S. Use the theorems and given information to show that r

A: The figure is as shown below : Given, ∠4 = (13x-4)o, ∠8 = (9x+16)o and x=5

Q: If x and y are elements of an ordered integral domain D,prove the following inequalities:   x2- 2xy…

A: x2-2xy+y2=x2-xy-xy+y2=xx-y-yx-y=x-yx-y=x-y2

Q: 3. Given: GH DE Prove: AFGH ~ AFDE F G 工

A: Given data: Line GH|| DE In triangle FGH and triangle FDE m∠F=m∠F  [common angle] We know that line…

Q: Show and use d(Xn, FCN))<« d(Xn-1 'x) Vny? To prove X = fx) %3D

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Q: 2, 5x .3 b) Y = In 60(х, + + X, 2. 3.

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Q: 3. Show that the function p : F → Ę which maps o to o is a bijection from F to Fe, where and ar to…

A: Let ϕ:F1→F2 be a function such that, ϕ0=0. Also given that ϕαr=β3r, where 0≤r≤6 When r=0,…

Q: @show that a) G (x,x) => Uu6) Unl) were G is green funcfion

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Q: Find the. Lo. T.of the non-peridic functon= oくtく」 f(t) =

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Q: T be the lineas translfomation et whose standasd matsine is A= 2 -2 2. - 2 Does T maps 3 3. R4 onto…

A: A=2-29203-230005

Q: verify that (AT )T = A

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Q: Verify that the function satisfies the three hypotheses of Rolle as a comma-separated fist.) x) = 3x…

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Q: Let a = : 3432, and b = 332. Find x, y € Z such that xa+yb = gcd(a, b). To get full marks you must…

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Q: AE Mmxn amed suppose be non Let that A=xY is the fall ragak factorization that At =x*y then Show

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Q: Show that f: R → R defined as f(a) = 3a³- 4 is a one to one %3D iuicuon.

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Q: Show that there is a real number t such that (e^−t) − (t^3) = 207/(t^4) + 1.

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Q: Show that ∗ : R × R → R defined by        a ∗ b = a + 2b is not commutative.

A: Show that ∗ : R × R → R defined by        a ∗ b = a + 2b is not commutative.

Q: 9:Find the absolute exlemum Verlues of flx) x²-4x+24 over the interNal Cl,41

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Q: 5. Find all pairs (m, n) of positive integers such that y(y(nm)) = n, where p is Euler's totient…

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Q: 1 and the domain for g(x) is a s as x-> inf, f(x) -> inf and the

A: Domain of a function: All the possible values of x that makes the function f(x) valid or the values…

Q: R. find he Corficient of

A: We need to find coeffiient.

Q: Let [a] be a non-zero element of Z43. w| 42. When is an element of Z43 said to be a primitive root?

A: This question is based on primitive roots. We recall the definition and give couple of examples.

Q: Find the absolute maximum and the absolute minimum of U(q) 20002 (15 5q)4 on the nterval 04.

A: First find the derivative of the given function and compute the critical points.

Q: Use the diagram shown. В C 主 G 丰 Which is a needed step to prove that AABF EAEDG

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Q: et whose A = T be standard matsix teans bormaton is the lineas 2. 3. Does maps R3 onto R4? s Ta one…

A: Given that T is a linear transformation whose standard matrix is given by A=203032005000. We have to…

Q: Evaluate the following. 5y + z S: z = 15 - 6x + 8y, 0 < x < 1, 0 < y < 3

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Q: Given the function z = In (2xy + e3x) - 5y, %3D az a. ax

A: Since, we have to find the partial derivatives ∂z∂x and ∂z∂y of functiongiven by z=ln…

Q: Prove the followling identites 9) A-7-A 2. gn gntt

A: a) Given, ∆-∇=∆∇ Take LHS, ∆∇fx=∆∇fx Since, ∇fx=fx-fx-h ; Here h is the step size. and ∆fx=fx+h-fx

Q: find the desivalive d the functian ha)= ainfse and compute h'(2) Th o

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Q: Use Green Theorem to Evaluate y x²dx – x²dy where C is left half of x² + y² = 25

A: Note that left half of the circle x2+y2=25 means the second and third quadrants. Now, in the second…

Q: Q1. Prove that KT = = -.

A:

Q: Classify the following ODE's with respect to order and linearity. a. 3x-y' - 5y = 7x³ - 8x+1

A: Given  a. 3x.y'-5y=7x3-8x+1b. xy2.y"-6xy'+2y=0

Q: Which of the following is not a notation for the dertvative of y In termo of x. dr f'(x) dy

A: to find the derivative we first write the function f(x) then write f(x+△x) and f(y+△y) therefore the…

Q: Q. Let flx)- if x20 07 xt Prove that fX) = 2|X| for r every X X

A: Given function is,

Q: Given: G is midpoint of IE 21 = 2 Prove: ATIG = AREG 2 1. 3,

A: Given that, G is the midpoint of IE¯ So IG¯=GE¯ ∠I=∠E∠1=∠2

Q: Let z = 2 - 3xy?+ x². Zay %3D Zyy

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Q: Let X=L'[0,1] and x=2()- Find Ilallp for P-4 and ∞

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Q: Use Green Theorem to Evaluate |y x²dx – x²dy where C is left half of x² + y² = 25

A:

Q: 3 Q7- Let fw=ex-y, Find a fun ction y =gcW So that f. 9) (x) = X+ 2 .

A: Given f(x)=2x3-4 To find a function y = g(x) such that  (fog)(x)=x+2