Find the cemplex fourth routs of Z: 2 J3-22

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: Find r'(t) r(t) = 6Vti + t²Vtj + In(t? )k %3D r'(t) = %3D

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Q: Suppose that f(r, y) = 3x y + 8a? + 4y? then find the discriminant of f.

A: f(x,y) = 3x²y² + 8x² + 4y² So, fx = 6xy² + 16x  &, fy = 6x²y + 8y  &, fxx = 6y² + 16 &,…

Q: M is the midpoint of AB 2x + 1 and MB AM = %3D 1 ond AM

A: Given;- M is the mid point of AB AM=2x+1 and MB=3x-2    Therefore, AM=MB 2x+1=3x-2 3x-2x=1+2 x=3

Q: Numerically integrate f(x) = x2 from a=0 to b= 2 using a multiple segment (n-2) trapezoidal %3D…

A: Trapezoidal rule  ∫abf(x)dx≈Δx2​(f(x0​)+2f(x1​)+2f(x2)+2f(x3​)+⋯+2f(xn-1​)+f(xn​))whereΔx=b-an

Q: Consider the lollowing inner prodact or R 2 by, % ニaメ, X X. + 2. Cし3)上63) oa tb = ?

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Q: Find length of the cardioid r-a03from 0 0 to 0 t %3D

A: To find Length of cardioid r=aθ3  where θ=0 to θ=π

Q: What is the domain of r(t) = e'i + j+ (t + 1)~³k?

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Q: Use the Runge-Kutta 4th order method to find the values of y where x is given that y = 1 when x = 0…

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Q: R. 4. Use the information in the figure and prove that VC = CX, making use of reflec- tions. [UCSMP,…

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Q: whot is the eq ualion ot thl taney @art lime to the fumctionfra fcx) = x+ 5x-2 at the point (-6;4)

A: We can find the equation of tangent as below

Q: If v.ổ = dox = 40 pc/m %3D %3D XP find D at x=5cm Q in the voleme OS x< 10, 53ys15, ○く2く 12cm

A: We have to evaluate the value of charge and D.

Q: the IVP ly a Sum of povers up to and including x5. cx-2) y'= xy, yroje 4 Q.6. Salve pover ceries and…

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Q: AB intersects CD at E. If the m AED = 6x - 20 and m ZCEB = 2x + 60, find the ZAEC. %3D

A: AB intersects CD at E. angle AED=6x-20 angle CEB=2X+60

Q: Find r'(t) = 8Vti + t?Vij + In(z²)k r'(t) =

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Q: 24yıy2, 0< yı < 1, 0 < y2 < (0, fV1, y2) = %3D elsewhere Find the cov(Y,,Y2) is it possible for Y,…

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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: Find the general şolution_to the following. (D* - 2D – 7D? +8D+12)y = 0

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Q: Prove that : V.(V×A)=0

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Q: %3D then przove that .cūxR=0 and vxcãuFR)= 2Ù

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Q: 3. Find the circulation of F 2xi + 2zj +2yk around closed contour %3D

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Q: (c) Evaluate ff. 2y² + 4z² ds, where o is the first octant portion of a cone z = x2 + y2 with height…

A: Here we have to evaluate ∫∫σ2y2+4z2ds where σ is the first octant portion of a cone z=x2+y2  with…

Q: Consider the IVP y" + 2y' + 6y = 0, y(0) = 2, y'(0) = 3 > 0. %3D %3D

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Q: (a) Evaluate APA: – 6) R where R is the solid hemisphere r² + y² + :² – 2r + 4y = 4, : 0.

A: We want to evaluate  ∫∫∫R9-z2dV where R is the solid hemisphere x2+y2+z2-2x+4y=4, z≥0 We can write…

Q: -3y(In x)' +3x* (In x) y' =0

A: First simplyfy the given differential equation.Then taking integral on both sides and solve it.

Q: Use L and L to solue y' t 3y= f4) y)=5, where f4), (32)

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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: Solve the PDE to find Z AZx + BZ, + CZ = 0 %3D where, Z(0, y) = e3y %3D

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Q: Find b∈R such that ∫∫Ssin (b) ydS = 8, where S is the part of y^2 + z^2 = 4 that is between x = 0…

A: To find the value of b satisfying the given integral.

Q: Integrate g(x, y, z) = x + y + z over the portion of the plan 2x + 2y + z = 2 that lies in the first…

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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: Consider P2 with the inner product = f (x)g(x) dx. Then d(x, 2) = %3D a) b) c) 2 d) LOom

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Q: Determine the voctor ficld of F. F(x, y) = 12i - 4j

A: We have to draw vector field of given vector.

Q: Evaluate p xy da + a dy, where C is the rectangle with vertices (0,0), (3,0), (3,6), and (0,6).

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Q: Write a in the form a = arT + aN N at t-0 for R(t) = t2i + %3D (t+r) + ( -r°*

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Q: H.w use Gramer Rule to Fird XIZ -2X-y+2 -3 %3D -2x43y- 221

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Q: Find the constants c0, c1, and x1 so that the quadrature formula Z 1 0 f(x)dx = c0f(0) + c1f(x1),…

A: Consider the given quadrature formula, ∫01fxdx=c0f0+c1fx1 here we need to determine the constants…

Q: Calculate the trapezoid approximation of 5dx using four subintervals. O T5 = 0.60 O T5 = 0.40 O T5 =…

A: The trapezoid approximation of the given integral is given below.

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

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Q: ニメ Find the eg uaton (x) 4a| %3D 3tan x when fo f the tor

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Q: |Agebraicaly soleforthe eat aueso l 3D1-0s%. Multple arswer shoud be separaed with commas, X3D

A: Given:  2cos2x=1-cosx     and x∈[0,2π)2cos2x=1-cosxlet  cosx=mthen             2m2=1-m2m2+m-1=0it is…

Q: Y = / x² g 4-Jx²_s %3D 2

A: Given function : f(x)=x2−94−x2−9

Q: Use the Midpoint Rule with m = n = 2 to estimate the value for 4x + 3ydA on the rectangle R = [0, 8]…

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Q: Consider the 2D domain D = (x, y)|y > 0, ; < x² + y² < x 1. 1 d(x, y) using / / Calculate dr d0 set…

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Q: QY Use Gramer's Rule to Find K,y and Z -y-22 =-8 %3D 1 + 32 = 2 %3D 7X +y+Z = o

A: Craners rule used

Q: Find the general şolution to the following (D* - 2D – 7D² +8D+12)y = 0|

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Q: Consider the finction f(x, y) = 6y² + 4x² – 12xy – 4y. Then:

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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…

A: Given