Find the exter ma Fr xy)= x² +y?- xy

Q: Given U(x; y) = In(1+ xy³), show that 2! dxðy

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Q: dp +t². dt For p(t) dw For w(u) = Vu - 2u? – 10, du

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Q: If r(2) = sin(z² – 10z + 16), find r' (z) =

A: Since, we have been given that r(z)= sin(z2-10z+16)Our Aim is to find r'(z)=?

Q: Evaluate : J x dx, where neN.

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Q: Ex. Evaluate ff y ds where S is the portion of the cylinder x + y = 3 that lies between z= 0 and z=…

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Q: Find dy y = e fin (52) for り =

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Q: Apply Uptimal obtain y, y₂₁ and y for the pr 3

A: given y'=t+2y h=0.1 and y0=1 to find the y1,y2,y3 proceed as follows Apply Runga Kutta 2 order…

Q: 0(x. y) y= Vuv , then find 2. If x=, at (1,1) O(u.v)

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Q: dy Find - xp x = t sin(t), y = t? + 4t

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Q: If f(x,y)=xe/2,+37x?y3, then dx²əy³ at (1,1) is equal to

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Q: d?F – AF = 0, dx? slove avec F(0) = 0, F(1) = 0 et aeR.

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Q: dz where C is the bo + 6)

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

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Q: If PQ = 9 and QR = 28, find PR. %3D %3D

A: We use  formula to find PR. PR=PQ+QR

Q: Evaluate . y? cos(x) dx + 2ysin(x)dy where C is the straight line between (0,0) and

A: The equations of the straight line joining (0,0)to π2,1 are x-0π/2-0=y-01-0=t(say) i.e. xπ/2=y1=t…

Q: EX:- Show that dw Vす 2. の ē" dw fcb)-VEerfa) %3D e dw ei

A: Using error function erf(f) .

Q: To which coordinate axes are the following cylinders in ℝ3 parallel: x2 + 2y2 = 8, z2 + 2y2 = 8, and…

A: The cylinders x2+2y2=8, z2+2y2=8 , and x2+2z2=8. We have to find to which coordinate axes are the…

Q: dy = Solve 2xy r x2 + y? given that y = 0 at a = 1 %3D

A: To find particular solution of D.E.

Q: 2. у"dy 3D х (хау — уах)еу 3. ydx %3D х + Vу? — х?dy 2 (1n In v) d, - y (1ulny ulnr) di

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Q: Given f(x, y) = 2x* – 4xy – 2y?, find frr(x, y) = fzy(z, y) =

A: Solving the problem by finding the partial derivative.

Q: Find the exact value of dyd.r.

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Q: ind a suitable A and B so that: A< S, Vx + 4 dx < B

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Q: Given f(x, y) = 9xy® – 6x*y. Compute: a?f ду? ||

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Q: Prove that r(v) : dx, v> 0.

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Q: ind if f(x,y) = y sin xy ax

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Q: Evaluate f ((x – y) cos(7(x + y))) dA where D = {(x, y) : Y < x < y+2, –x < y< 3 – 2}. D

A: Solve double integral by using the change of variables

Q: FIND a-b - Ci FOR b>o GIVEN PS : f(x) = E [n! (2x + !.)" ] WITH: %3D h=0 ROC : R=q Ioc: Sb A.

A: We will find out the required value.

Q: Je b. Find of f(x,y) = ye*"? ax' ay %3D

A: Use logarithmic differentiation to solve it.

Q: dy x fanx

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Q: dz where a inside r= C z-a 2ni

A: We have to find integration of given function Using Cauchy's Integral Formula.

Q: dy Find given y = xcos).

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Q: Find r'(t) r(t) = 6yEi + t²/ij + In[? }« %3D r'(t) = %3D

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Q: exy w = f(x,y) = ² sing Rind all P.D.

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Q: g(x) = Af(Bx), where: %3D A = %3D B =

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Q: "ind y' xy =; ху • y = v? + 2v y = V2x² – 4x +1 y? = x +y+ xy ,v =

A: “Since you have posted a question with multiple sub-parts, we will solve first three subparts for…

Q: "ind where f(x, y, z) = e²´y and x = Vuv, y = ; %3D dv

A: To find the partial derivative using chain rule

Q: 11. f (x, y) = ery subject to a? + y? = 16 %3D

A: The objective is to find the lagrangian multipliers for fx,y=e2xy subject to gx,y=x2+y2-16. To solve…

Q: . Evaluate ry² dA, where D = {(x, y) | sin r < y s 1/2,0 <S7/6}.

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Q: SOlve the inihal problenm. shouid be in Porm y=--. -3 dy = (38t+51) dł Y () =0 %3D

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Q: If f(r, y) da dy = K, where K is a constant, then 5 f(x, y) dy da: %3D ок O-K

A: Solution: The objective is to find the value given integral

Q: BD = 10, GF = y, AC = 4, AF = X %3D %3D y D

A: From the given figure BD=GE And Chord of equal length are equidistant from centre  Therefore, AF =…

Q: Find . for (x,y) = x² + y² af af ду' дх Find ду' дх Je Je for f(x,y) : sin xy? x2+1

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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: Find dy/dr if y = r In(x). Answer:

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Q: f (г, у) — In(ax + by) a, b ER af Land 1 Find Ja 2. Find and a f -and 3. Find dxðy дуда

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Q: For x=In /t y=2, find y" when

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Q: If Jf(x)dx = cotx? +C, then f(x) is equal to

A: ∫f(x)dx=cot x2+C

Q: Evaluate ſ z dz, where C is given by x = 3t, y =t²; –1<t< 4.

A: Let us consider a complex function f(z) then the function can be written in the Cartesian coordinate…