Evaluate the t resiake theerem 2 allowing real infegrals by dX ans : こ。(X+a?)2 493 • I= F ans 8 (x41)(x+9) 12

Q: ExJ Describe the values of aoia, and ag such hat + Qi fj + Qg f +2. Furthermore, find the eror term…

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Q: Findif z = In x + Iny,where x =24e2 and y = 15et Enter the answer in the space provided. If your…

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Q: Q4) ut A = :) al let fox)- 2x_4x+5 and g(x)= x?42x + 11, Fiind + 2X + 11, Find @ A ; DA ; © PCA);…

A: Hello. Since your question has multiple sub-parts, we will solve first three sub-parts for you. If…

Q: Evaluate fSS, 5y²dV where E is the reqion below x + 3y + 6z = 9 in the first octant.

A: we need to evaluate the triple integration. For finding the solution first we will find the limits…

Q: Q4) Find the deviva tives of the follocoing (9) y = ( In xe) %3D (b) Sec ( ²+1 %3D

A: Part A -  We can observe that the power in the expression on the right-hand side contains the…

Q: tet z lbe defined implicity as a fyction of Ÿ andy by the equatioy ) ē+ coscxy) = (4-32)(2+28) 9. |…

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Q: Evaluate the Ś Ŝ (x²+2xY+ y% ) dy de when Step Size of xz0.2 and step of y=o.5 ? (use -> Trafezoi…

A: let f=∫01∫02x2+2xy+y2dydx with step size h=0.2 we have x0=0.2 , y0=0.5 fx0,y0=0.22+2×0.2×0.5+0.52…

Q: af find given f (x, y) = e + 2xy² - 4y at (0,3) 9 ду O-12 O-7 O 8 O 4

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Q: 10e? dz by residue theorem, where C'is the contour z| = 2 1:4 + 52ª Evaluate

A: Complex integration

Q: EX. Evaluate the JoJex*+2xy+y*) dydx when step size of X = 0-2 and step size of y=o.5?

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Q: 10e dz by residue theorem, where C is the contour |2| = 2 Je 1z4 +5z3 Evaluate

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Q: D Express the interval in (a-k, a+R) aad 1 x.-alc.R I(3x+1)?(<!

A: |(3x+1)2| &lt;1 both side we take square roots |3x+1|&lt; +1 3x+1 &lt;+1 3x+1&lt;1    or    3x+1&lt;…

Q: If f(z) = cosh(In z“), then f' (7) = %3D %3D Your answer should be rounded to the nearest whole…

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Q: Isint t this equal to-. f(t) will noy+"|72 7 74155 = (+) JT W 17 750)

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Q: 04. Show that T = satisfies the equation T + Tyy = T³. %3D

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Q: The Cornev 8-I make outbound A, B. 3. achieve Ax-u38/--12A.B %3D Otrue 2)Err

A: We know that  a×b represent vector product of two vector a and b  a.b represent scalar product of…

Q: Q4: (a). Prove that u = 2x(1-y) is harmonic.

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Q: p* + 51³ + t² + 5t + 5 -dt = 1? +1 (Type an exact answer, using t as needed.)

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Q: c) Show thiat det a q² -k-1)(61)-) I <a<b %3D

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Q: An enclosure is to be built adjoining a barn, as in the diagram. The walls of the barn meet at 135…

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Q: b) Find v²f where f = e²x sin2y. cl Write the sufficient condition for ovistence of Lapla

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Q: e) Use (; a²p Find the value of Vm at which both of these deriva- T to find aVm tives are zero.

A: I will present e bit for u in the last step....inorder to show u the steps clearly of e bit , I have…

Q: f. . Prove false by creating a counterexample: 9(AUB) C P(A) U P(B)

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Q: dy Find Do not simplify. d.r 5sin- (a) y = cosh r Vsec z + In 7

A: Given that: (a)y=5sin-1x-coshxsec4x+ln73(b)4x3+lny=excsch(2-y2)

Q: az a2z az a2z at ax2 23. If z = sim(x+ sint), show that дх дх дt

A: Given,Z=Sinx+sintto prove∂z∂x·∂2z∂x∂t=∂z∂t·∂2z∂x2

Q: O i using The( 3) uence Xm>is

A: First we have to show that Given sequence is monotonic and bounded then it is convergent

Q: One 56 Use fPicard method to approximate y when a= 2, given that y=1 when r=o and dy da

A: The function f(x) is a rule that associates or fixes a number to the particular point x. If y=f(x),…

Q: Comsder the qunchion g: [-3, 0) to R dezined! by gex = (x+3)?+s 'Fnd y guny pl and thoding its…

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Q: If z = u", then dz is equal to: du

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Q: What is the tangent of 0? 6 D 6V11 11

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Q: a: Find theintervals. oA the hundionon which, iacreafing onwhich Jecreasing oncd Phe inteneds ①…

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Q: const at Verify 4=(e~x-I is the gereral solticn

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Q: Evaluate J by means of trapezoidal rule using n = 10 and n = 20: 1 J = exp(-x²)dx = Se

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Q: Q2: Employ modified secant method to locate the root of f(x)=sin (Vx ) - * Use an initial guess of…

A: Modified secant method iteration formula: xi+1=xi-δxi·fxifδxi+xi-fxi Given: f(x)=sinx-x, x0=0.5,…

Q: Q3) find tne u bait ve ctor Pointing for ACe,3) to the (0,0)

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Q: %3D otheowis Jiven that Pa) is apd f O find c ?!

A: 1) The value of c is obtained below: Given pdf is, f(x)=cx, 0≤x≤2 ∫02f(x)dx=1∫02cxdx=1   cx2202=1…

Q: 2e Evaluate dz by residue theorem, where Cis the contour 2 = 2 c 9z4+45z3

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Q: Q2 Find fr and fy for the following funetion: f(x,y) = + In(5x – 3y).

A: We find value of fx and fy of given function f(x,y)

Q: L"f(t) dt = 8, Lif(:) dt = 1. Find 9. 8. Can not determine.

A: According to the rule of additivity of definite integral:

Q: the rAm t twico a and b A Jumby! f(x]=X-/ a(x)=5xj What is tglx)?

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Q: Find the imaginary part of the analyhc funckon,whose real part is : sxy? 3x²-34?

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Q: B) f(x) = x+3 (-6, 6<x<1 Is f cont. at x-6?

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Q: V- Assuming Cov(X, u) = 0 allows us to equate Ex û to zero. True or False? Explain.

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Q: dy +. (x>0) tind the Soiution of the difperential equation, expressing 4explicitly as general 4…

A: First we comparing the given differential equation with dy/dx+Py=Q .and then find I.F. and then…

Q: mZF=90° DE = V113 DF = 7 EF = 8 What is the value of cos W? O A. 7 O B. 8 7 OC V113 O D 7 V113 P…

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Q: find f (a ) if you Kinow that f'cz) = (1+tanz)sec"x 3 2. and that f(o) = 54.

A: dtan xdx=sec2x ∫ax+bn dx = 1a.ax+bn+1n+1+C

Q: Let (-) - {. S 8x², x 9 Find the values of a and b so that f will be differentiable at x = 9. а i b…

A: For differentiable function, left hand derivative is equal to right hand derivative

Q: S Integrate the falloing funclinne the given kesinms aver R: y=4x-x and y =X

A: Area