lo J (r +1)² + 2(y – 4)² = 12 (с) y? – 8y 4х — 16

Q: If f(x, y) = 5y² – 7xy+ 14x, then is given by: - dy? O -4 O 17 O 10 O -10

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Q: (2у? + 4л?) da — rуdy — 0 - %3D

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Q: Find r'(t).

A: We have to find r't: rt=4ti+t2tj+lnt2k We know that dxndx=nxn-1d lnxdx=1xd lnfxdx=1fxd fxdxdxdx=12x…

Q: S' SI S*** 12xzdydædz=? I+z O a. 2 O b. -2 O c. 1 O d. -1 O e. 0

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Q: Find a particular solution to： y''+5y'+4y=10te^(4t) y(p)=?

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Q: R m 1 Uo 1 2Tr dr TR²

A: Follow the procedure given below and use simple integration principle.

Q: The DE : y'= e 5x-7y is seperable Select one: O True False

A: We have cheek

Q: 3-Evaluate Fdr where 2X Cisgiven by rit) = t3+U-3t)rék

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Q: 2. s - [GpAq)Ar] = a. 7 [(pV7 (qAr)) As] b. (pV7 (qAr)) As с. (pV (qAr)) d. None of these

A: The given question has been solved with explanation in step 2.

Q: 5. Find the general ne given DE! 2x + 2xy2 dy y + 2x?y dx A. 1+ y? = C(1 + 2x2) B. 1- y? = C(1 +…

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Q: y aln(a) – y = 0; y(2) = In(4)

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Q: Oy" + 0.54y' + (0.0729 + T)y = 0 %3D

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Q: x=In i y=r2, find y " when For x=0• O 8 O 4 O 16 O 2

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Q: What is the particular solution of (3y? + 10ry?) dæ + (6zy - 2 + 10x?y) dy = 0 when x = 1 and y 2 ?…

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Q: Solve (x² + 4)y' = 2xy In|x] = In(y? + 4) +C O Option 1 Inlyl = In(x² + 4) +C

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Q: 1 Evaluate dz, where (i) C is z+ = 2 .2 +1 C

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Q: The solution of the DE (4xy -3)y' =-2y² -1 is 2xy² + x – 3y = c O None of these 2хy? - х - Зу 3 с…

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Q: J) 11"+2 + 122n+1 divided by 133 , Vn E N*

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Q: dz where C is ned by x = 0, :

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Q: iS (2) = (x + ay² – 2xy) + i(bx² – y + 2xy) is anal ytic, then the values ofa and b is

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Q: z2 = 9 and outside the cylinder x? + y? = 1.

A: coordinates, x=r cos θy=r sin θz=2 x2+y2=r2cos2θ+sin2θ=r2x2+y2+z2=9r2+z2=9⇒z=±9-r2 x2+y2=r2⇒r=2

Q: J!J+*+*+z²dv ,where E{(x,y.2)/x +y* +z² s4}. O A. 647 O B. No correct Answer OC. 207 O D. 10247 O E.…

A: Given: ∫∫∫E4x2+y2+z2dV , where Ex,y,z|x2+y2+z2≤4

Q: -dz < 2re?. z + 1 Jェ-1|=1

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Q: JJJ Y G inder r2 + v2 = 4y bour inder

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Q: r In y dr, where D is described by 1 < r < 2, e <y<e aD | V1 +r² dy, where D is described by -1<r<1,…

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Q: If z = x + jy, where x and y are real, the value of lei is OA. 1 OC. ey OD. e-y

A: I am providing the detailed solution of the first question only : as per our guidelines.   We will…

Q: What is the general solution of zyda - (2 +3y) dy = 0 ? O a + oy In y Cy og In y = C 6y Iny cy? Quiz…

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Q: C is given by x = 4t and y = 3t, where t runs from 0 to 2. Evaluate (y/x)ds 45/2

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Q: . In WXYZ, WX = 10. What does ZW equal? %3D а. 16 b. YZ с. WY d. none of these

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Q: y = 2teat²+bt+c y = t°e? y = (at³ – 3bt)² y = In(ax)e²x

A: As per our guidelines we need to solve only three sub parts. Please repost the remaining subparts as…

Q: dz, C:z| = n. %3D 2++13z2+36

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Q: d²y Compute dz? at the point (1, 2) given a² – y² = -3. a) 3 b) 4 9 d) 8 e) O

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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: dz wher the integral fe z2 +9 C = 4 is

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Q: S- - ydx + xdy, C: y² = 3x from (3,3) to (0,0) 01 0 3 O 0 2

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Q: Solve the eauation In(2x + 2) – In(4) = 2ln(x) O a. x= 0 O b. x= 1 O cx= 2, 1 O d. x= 1, -1/2

A: Given,, The logarithmic equation  ln2x+2 -ln4 = 2lnx  We have to solve the equation.

Q: S T6 dar = tan-i +C 1 –1 16+z2 4 True False

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Q: dr if r= Vs+1 dt and s=16r² – 20r 1. Find - %3D

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Q: Evaluate | (r + y)ds, c : x 3t, y = - 3t + 3, for 0 <t< 3.

A: Given: ∫C(x+y)ds, C: x=3t, y=-3t+3, for 0≤t≤3

Q: • Which of the following is z when dz 3.r + 6y² + 4? a. 2 = 4x + 6y? + 4x b. 2 = a + 6xy? + 4.x c. 2…

A: Solution

Q: 1 What is h(z) dz? 2ri C4

A: In this question, we evaluate the complex integral by using Cauchy integral formmula.

Q: dy Given y = 2u? and u = 8x – 1, then dx - 8(64x? – 2x + 1) 0 خيار 4 48(8x – 1)2 0 خيار 3

A: The derivative of xn is calculated using the formula, ddx(xn)=nxn-1 .

Q: dx = In + V4- r +c O True O False

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Q: What is the general solution of xydx (a? + 3y²) dy = 0 ? - + 6y? In y = Cy² 6ylny = cy? O 2? 6y? In…

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Q: te² i· k) dt V1 – ? 40.

A: Solving by definite integral we have

Q: What is the general solution of xydx (22 + 3y?) dy = 0 ? - 6y² In y = C 2 + 6y? In y = Cy? 6ylny cy?…

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Q: rer, Evalua den (3x1 fnd C: lve Segeant Co0) to (4,2)

A: Line Segment:    Each portion of the line segment can be labelled for length, so you can add them up…

Q: Solve the following DE: (2xy + 3x²) dæ + (2xy+ 4y) dy = 0 O a²y? + x³ + 2x?y? + 4y3 - 2xy = C O a'y?…

A: Solving the given differential equation

Q: 2. Given y = 25e-2x verify that y' + 4xy = 0 Your answer

A: