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Q: Is it true that for cont. f So Si Axy)dydx = fS, Axy)dxdy| Justify your answer

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Q: Q Find the Probabi litty of finding aclosed patht f m if the probebiltyof Switching onf f •f

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Q: Let A be a cut. Show that if r ∈ A and s /∈ A, then r < s. To dispel any suspense, let’s get…

A: Consider the definition for the Dedekind cut A.

Q: Determine if the Sóllowing justi fy by egprvelent: 1. Ore showng work. and ムx-2 2

A: Given:  12x2 - 4x / 2 and  6x - 2

Q: Verify that fxy = fyx for the following funtion.  f(x,y) = ex + y + 1 fxy = ? fyx = ?

A: Given,            fx,y=ex+y+1

Q: r próducts, šó thát théy indeed. They took an a ts to explore the claim -ies randomly.

A: Let X be the random variable such that the life-length of the battery producer company fabricates.…

Q: (c) Is ergodic (d) Is wide sense stationary

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Q: Find fx for f(x, y) = In(x – y).

A: Given that fx,y=lnx-y To find fxx It can be found by fxx=∂2f∂x2     =∂∂x∂f∂x

Q: Find y" by imprcit differen fia fên. Simpliey unenoven Po Ssiole

A: Given:- x2 + 9y2 =9  To find:- y'' of given equation

Q: Find fry for f(x, y) = In(x – y).

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Q: Give an example where | f(x)dg(x) exist even through f is unbounded on [a, b].

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Q: Show that f(x, y) = point (5,-3). 3x+2y x+y+1 meets the three conditions for continuity at Add-ins…

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Q: Use the Trapezoidal Rule with n-6 to approximate. f(x)=sim2x.a=0,b=π

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Q: Q6:-Prove that: y" = 1 if y=;csc (tan"

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Q: Find the fonction f(x) that Satisfies the Fallowing difforential equation and initin) conditions:…

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Q: F ind the oua gohenegion Aounded ky メ=y,メ=13-が 2 x=18-y (0,9) てっ (,) Une borizontal ilement to firid…

A: The area of the region can be calculated using the formula , where is the curve of the first…

Q: Evaluate divergence VA when A = 2xay + 3yay- 4zaz and V = xyz.

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Q: If f (s Continuous then on -fex) True or felse?

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Q: The domain of f(x,y) = In xy is points (x, y) in the first quadrant Select one: O True O False

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Q: Let f(z) = (9 sin z + 2 cosz)tan¹z

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Q: In ΔFGH,  FH is extended through point H to point I, m∠FGH=(x−2)∘,  m∠GHI=(4x−5)∘, m∠HFG=(x+19)∘.…

A: Given that     FGH is triangle. FH is extended through point H to point I .

Q: et A be 4X4r nas non-brivial . -son-

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Q: ind the values of c that make f continuous everywhere: { Sa² – c² if x 3

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Q: 1f itwas x25ect, yatunt prove Thut dy

A: Simple derivative

Q: O No, because f is not continuous on the closed interval [a, b].

A: Given that: The function f ( x) = x2 - 81x - 4     ,  [ -9, 9  ]  .

Q: Use the difinition of error function Prove that: 5(1/₂/2) = 5T let: ere (x) = 33/3324 dt

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Q: Let f(x)= Find f'o. Hint: do not evaluate the in tergral,

A: We will use the Leibnitz formula for differentiation of an integral.

Q: O Evaluate the foll owing in tegrals: Ins 2x+y (Sinztcany) dx dy In2 e dydx JA ROSISu, Isys2

A: “Since you have asked multiple question, we will solve the first question for you. If youwant any…

Q: Use the continuity test to verify which of the following fur specified points. a. y= X-2 3x at (i) x…

A: Given function: y=1x-2-3x,      x=2, x=-2   Continuity: Let fx be the function defined on the domain…

Q: Consider (Ru) .f : R->R -3 X3o 3. X70 Prove Pex) is Con tinuos onR-301

A: Given that                                      f:R→Rf(x)=-3; x≤03    ; x>0 we have to prove that…

Q: So So t² etu du dt

A: Given, ∫03∫0tt2etududt

Q: Get the Ist order DE the falloing (3xy-Hy-1Ddx= -x(x-2)dy %3D

A: As per our guidelines we are supposed to answer only first question. So i have solve  first one.…

Q: Consider the following. -8x, fx)=2- 8x + 5, X > 6 Find the x-value at which fis not continuous. Is…

A: Given function is f(x)=-3x               x≤6x2-8x+5      x>6 The function is continuous at point…

Q: find he querage vallwe of he fanction z-cor ox m De mternal ( )

A: fx=x-cos26x,   0, π6.

Q: Find the radivs of Conwergence for

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Q: the following "quation sutisfied Cauchy - Rieman equation es .4 W = Z

A: The general form of a complex number is given by z=x+iy, where x,y are two real numbers and i=-1.…

Q: O Evaluate: | (In a + xe" + Vry) dy

A: Solution of the problem as follows

Q: 4) Fund the interval of x-value on which the Carve is Con Cave up and Con Cave dawn 3 fex) = +x-3X

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Q: Find the discontinnity point of &Cz): ニ そzそ+

A: Given that, the function is fz=z+1z2+2z+1. Set z2+2z+1=0 to find the undefined points. Compare the…

Q: What is the net crarop for fW={+5,05 as we qo from x=2 to X=5?

A: The given function  f(x) = x2 + 5

Q: a²z If z = arctan ), find ( ay?

A: Given,           z=arctanyx= tan-1yxTo find           ∂2z∂x2+∂2z∂y2=?

Q: Use the Midpoint rule to deterine the Intergral for the error Function (erf)(belou) 4caurete to…

A: ∫01e-x2dx here we can take 4 interpolation point so n=4 so h = (1-0)/4 = 0.25 x0=0 x1=0.25 x2=0.5…

Q: find the X-ualues (f ong at which f1s not Continuous, which of the discontinuities are removable?…

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Q: Use cubic interpolation method with two points to find uz , where a = 0. 6, h 0.1, ɛ = 0.001 and O'…

A: Cubic interpolation method gives the following formula for evaluation, For, μ2=a(∅')-h1+∈ Therefore,…

Q: Consider o Com Assume He holding holding 入, thot s Vo =VI = to the ofher going 1. Draw the rates,…

A: 1) Given that the continuous Markov chain has two states s= {0,1}. The holding parameters are given…

Q: l? sc tue suell metuozd to fired tue voune of te Solid genented the by rerolning the plene rgim…

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Q: d'y on of x

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Numerical Integration

In a mathematical investigation, numerical integration comprises a wide group of calculations for computing the mathematical estimation of definite integral, and likewise, the term is moreover in some cases used to depict the numerical solution of differential equations. The most important aspect of this theory is error analysis.