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

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: d) Let y= Acos2t where A is a constant. Find the value of A such that d y --3y = 9cos2t for all…

A: Given  The equation is  y= A cos(2t) , where  A  is constant  and condition is  d2ydt2-3y=9cos(2t) .

Q: Find where 1)let . V°g r = l7| -- g(r) = In(r³) s = xi + yj + zk * vo x Vp 2) find = yz + zx2, P =…

A: Gradient and cross product

Q: Suppose that f(x, y) = e-2r² – 1y² + 2x +8y then find the discriminantD= faz fyy – fay- Question…

A: Solution: The objective is to find the discriminant

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: 3. PS bisects ZP of A PQR. If QS = 2x - 4 and SR = x+1, PQ = 8 and PR = 5, find the length of SR and…

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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: -R show that D-2D-31 =0 and hence find D", (b) Given that D %3D

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Q: 54. Find numbers a, b and c such that x = 1 + at y = 2+ bt is perpendicular to 2x + y - 3z = 1 z 3+…

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Q: 03. Find se and *. If f(x,y) = 2e* + Iny² ,and x = 2t + r2, y = ; %3D at r+1

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

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Q: af Given f(x, y) = In(6x² + 8y²) then %3D

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Q: dy 24. Find dr? in terms of x and y. 6-8xy 9x-5y %3D

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Q: 2 x 9 = +9 dy %3D

A: As per our guidelines only one question can be solved. The solution is given below for the 1st…

Q: 6e dz by residue theorem, where C is the contour |2| = 2 Evaluate 524 + 25z

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Q: Where Express AB Ас OM A 40A Ac SA X m = midpoint M = OA Bm Prove that = а = b = in terms. m 5 Bc…

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Q: Evaluate xy ds, where C is describe by æ = 4t, y= 3t, 0 <t<1. Enter your answer as a number in…

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Q: 5. By making a suitable substitution, find the general solution y= y(r) of the ODE dy = (y – 4r –…

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

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Q: ∫(5e5√y/√y)dy That is 5e to the (y to the 1/5)

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

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Q: d²y Given that x +y³ = 2, prove that dx2 4.

A: Given: x3+y3=2   As we know that; The Power rule: ddxxn=nxn-1 The Quotient rule: fg'=f'·g-g'·fg2

Q: (d) utt Q2: Use separtion of variables to find product solution for du 3 +x dy du

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Q: What is the value of x in (2x - 1) + j(x + y) = (y - 6) + j(2y - 4)?   Answer in rectungalur form

A: We have: 2x-1+jx+y=y-6+j2y-4 Comparing both sides: 2x-1=y-6                  ....(1)x+y=2y-4…

Q: Use Cramer's rule to solve for x. 2x = 3y – 47 + 11 9x + y = z – 1 Зх — 4у %3D 7

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Q: If f(r, y) = (3r" + 21 – 12)', then fy is given by : %3D

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Q: Find Duf at P. f (x, y) = 3(1+ xy)/"; ху)"%; Р(3, 5); и%— 1 1 i+ j V2 u = NOTE: Enter the exact…

A: Given function is  f(x,y) = 3(1+xy)3/2 and point P(3,5)  And u= 1/√2i+1/√2j  We have to find out the…

Q: d²y Given that x3 + y³ = 2, prove that 4x dx² y5

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Q: Find the extremal for -T | (2? + 2ri + 2r?) dt when r(0) = 1 and T = 2 (i.e. r(2) free). %3D

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Q: 2. Evaluate (3xy+iy²)dz along the straight line joining z = i and z = 2 – i.

A: Given the Integral, ∫i2-i(3xy+iy2)dz We, know that z=x+iy ⇒dz=dx+idy, When z=i    ⇒x=0 and y=1  When…

Q: 16. QT is a midsegment. Find x and y. PT = x- 10x, TS = 24, QR = 6-y, PQ = 2y+ 3 R

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Q: 3. In APQR, PX bisects ZP. If X lies on QR and RX = 10, PR=25, and PQ is 1 more than twice QX, find…

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Q: dy dr² in terms of x and y given that 6- 7xy = 6x - 7y %3D 22. Find

A: Given that ,6-7xy=6x-7y differentiate this equation with respect to x ddx(6-7xy)=ddx(6x-7y)…

Q: 6e? Evaluate dz by residue theorem, 9z4 + 45z3 where C'is the contour z = 2

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Q: z) = x' - 4r – 12:r² + 32z + 1- by commas. Enter exact values, not de

A: Find all the real zeros of f(x)=x4-4x3-12x2+32x+15. Given that f(-3)=0, f(5)=0

Q: Q.1) Evaluate, (a) 3y In (y) dy 7+1 zp- (ь)

A: Find the integral

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: 37 Го fо7 (xsin(у) — усos(x) dxdy %3D 2 2

A: ∫02π/2∫03π/2(xsiny - ycosx)dxdy in this this is double integration so in first we take y as constant…

Q: f f Find Af = where f(r, y) = In (9r2 + 5y2 – 3r). %3D

A: Here f is two variable function .To find ∆f , first calculate fxx and fyy then add them.To find fxx…

Q: af when s = 1,t = 1 for f (x, y) = x³ – 3xy - 6x + 6y ,x = 2t + s, y = 2s – t. a) Find as

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Q: dz when z 2x+15y, where x t-s and y=t+2s2 Find %3D Enter the answer in the space provided. If your…

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Q: 1 dz, when C:z| = 1 is Using Cauchy's residue theorem, %3D (z-1)(2+2)2 O a. 0 O b. 27ri Oc. 2ni 9 O…

A: The solution is given as

Q: Find the are length of f(r) = (r + 3)2 from r = 0 to x = c in terms of c. %3D 2/3

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