Perform the following in fóy (2y2 -3y4, -1/2 -3/4 3.

Q: y = x uonenba au udei6 wan pue suonnios jo aigp) P 12nnsuon

A: we can insert x values to find out y values for the table

Q: S (2y-3) dy 2y ³-y²-27y + 36

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Q: d by f(z) = (x alytic, then C %3D

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Q: a) FVoa = ? PMT - 300 r= e 4%=0.04, Az0.04 12 2 0•00333 %3D 5x 12 z 60

A: According to the given information, it is required to rewrite the answer. For part(a)

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

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Q: Q4) If VZA = |, such that AAT = 1. Find x? %3D %3D

A: Given that 2A=1-1   -1xT  such that AAT=ITo find x:

Q: Eliminate c from the equatia cxy + c²x + 4 = 0. O x* (y')? + x?yy + 4 = 0

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Q: Q2/ A/ Find the and ar * iff (x.y) = x - xy, x=r² +s and y =r-s as

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

A: inverse of matrix

Q: FInd the implicity differentiate x^2- 4xy + y^2= 4

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Q: Q6. Given M = {(x, y), 1 < a² + y² < 4} c R². (a) Determine dM and aM. (b) Is M connected? Pathwise…

A: On the set M, we have to find the following results.

Q: Q3) If f(x, y") = x + y? + Vãy find: af(x²y) and Ty) ду afxy)

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Q: 49y = t ²e-7t as the independent varie and c₂ as C₂ as arbitrary con

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Q: Es, given that x(0) = -1, and y(0) = 0 *+x+2y-1=0 2x+y+y-2=0

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Q: dxdydz Evaluate 'V1-x? NI-x²-y² V1-x2-y?-z2

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Q: Evaluate ze -dz, where C is z+ 2 ((+2+2)?

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Q: Q3 Evaluate fII, xyz dxdydz, 3 < x < -2,0 < y < 1,0 < z S.

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Q: D={(x,y):4 < x² +y² < 81,< x <-V3y}, V3 Find [S, dA JJp y2

A: We will use polar co ordinates to solve the problem

Q: Q2 Given that z = 8x2y - 2x + 3y, x = u v, y = u – v %3D az az and ди Find av

A: To find dz/du and dz/dv.

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: aw b- if w = x + 2y + z2, x , y r2 + Ins and z = 2r , find the value of ar .rk)

A: We will solve the following

Q: Q3. Let A = {(r, y), 4x² + 9y² < 36} C R² Is A connected? pathwise connected? Justify your answer.

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Q: y" + 4y' = 3sin2t + tcos2t %3D

A: The solution for the above question is as shown below.

Q: Find f'cx?, f"cxx) wheve fcK) = xe -2 Jc %3D

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Q: Evaluate -5у-5 dy 31. Jv+2y-4

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Q: 2,t-3P dt, then %3D 12

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Q: x3y5 Q3: Let x = 2 ± 0.005 ,y = 10 ± 0.01,z = 20 + 0.01 find u = %3D And fined the error ?

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Q: ,-(ax²+2bxy+cy²) dædy = e (Hint: Let s = x+By and t = yx+8y, where (ad – BY)² = ac-b². Then ax?…

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Q: The discriminant of ax? + bx +c = 0 is defined by-

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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: or the DE y' = xy2, y(0) = -1. Then, y(2)=

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Q: O Evaluate, (a) / 3y* In (y) dy

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Q: B = {(x,y xs2, -a sy s3, 0£21} SS, x*yz²dV 2 'B

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Q: Which of the following symbols denotes the operation of antidifferentiation? A) C) E B) F'(x) D)

A: In calculus, an antiderivative, inverse derivative, primitive function, primitive integral or…

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

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Q: Let * = 3.54, and y 3.31. Determine the value of C when you evaluate %3D 5+x xp-

A: Given ,y=∫x5+xdxSubstitute…

Q: if y=Asinx+Bcosx then prove d2y/dx2+y=0

A: Given,

Q: B) Then show | x + y|<|x| +1y|

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Q: af Find y dy √y+2 using the substitution u +5=√√y+2.

A: Follow the procedure given below.

Q: Q5: Let A = 7i – 4j + 2k and B -3i + 6j – 2k. %3D %3D - Find A + B, |A – 2B|, A × B?

A: Given: A=7i-4j+2k  and B=-3i+6j-2k

Q: If x – y = 4 and xy = k what exp ression is equivalent to x² + y² ?

A: We have, x-y = 4                           ......1xy = k2                             .......2 To…

Q: as Find w = 1° + 2y? I = r - s; y=r+2s2

A: Given:w=x3+2y2x=r-sy=r+2s

Q: = -4rt ; when t = 0, r = ro 1. 2. xyy' = 1+ y? ; when x = 2, y = 3

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Q: d²y If dx2 -n?sinnx , (y" = 0,y = 0 when x = 0), then: %3D

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Q: - (3x + )*. Let y Then - A(Ax + +)" (8 -)", where B dy = Al 8x + xp A = B = C = D = I| || ||

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Q: nimize Z = (-1)*(X, abjected to, X, + X2 + X3 s 7 + X. - Xo <-

A: Introduction: The Simplex method is a method for solving linear programming models by hand by…

Q: differentiate. a) g(t)こ3-2t St +1 c) H(u)= (u-JJ) (utro) d) FLt)- モ-3 %3D

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Q: Evaluate the convolution between h(t)= e2u(t), and x(t)=2u(t).

A: From the above details we have,

Q: fud the general Schiklen for the P+q =X+Y+Z

A: p=dzdx and  q=dzdy Let f(x,y,z,p,q)=0We can relate this equation to F(x,y,z,p,q)Then we have the…

Q: Use the chain rule to find where First the pieces: End result (in terms of just t): d = 江 西 血麵| 2 =…

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