(x²+y2 ) prove ne du + y ax -2 sin2u ( Euler's Rule) 5. If u = cot-1 that x ду x+y

Q: Find dz given:Za fixry}==x+2xy+4y2

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Q: Verify that the conclusion of the Clairaut's Theorem holds a) z = sin(xy) b) z = sin(x - y) c) z =…

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Q: dx - x³)². (1 – -

A: Solution: Let Then, singularities  of  f  are  given by…

Q: c) y = (x-2) 3 x² (x-1)(x+5)4 [Hint: use logarithmic differentiation]

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Q: (7) 3x-7>11 ans./ (-co, -4/3) u (6, co)

A: Disclaimer: "Since you have asked multiple questions, we will solve the first question for you.  If…

Q: prove that 2. = - Cotx + C 2 |- Cos?x + Sinx

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Q: 4) Let f(x) = - ax"+1 and a x) = 4X-3 5:) f(x) = Fxan? find the 3 first f,g and h. uch that (fo gohl…

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Q: If u = x3 -3xy and v= 3x2y-y3, prove that Pu/Əx2 + Pu/əy2 = Pv/ax2 + Pv/@y²

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Q: Find Domain and Range бяц tue Ⓒsin (x+3) +2y x²+2y 3x + y² 3) 3x + Sin (3x) +2y+Z² Ⓒ x+2y cos2x…

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Q: (b) If f (x, y) = y sin2x + x°cosy °cosy 3 then verify dxðy dyðx

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Q: valuate the integral using U-substitution x dx (7x2+3)5 1) S A)-(7x²+3)-6+ C C)-(7x² + 3)-4+ C…

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Q: 3. y" = Vx3 4. у" + 16у %3Dsec(4x) — 3

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Q: cos2x a) -.dx,b) xe*. dy Į sin2x. [In(sin2x)]² + sin2x 0.

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Q: az a2z az a2z at ax2 23. If z = sim(x+ sint), show that дх дх дt

A: Given,Z=Sinx+sintto prove∂z∂x·∂2z∂x∂t=∂z∂t·∂2z∂x2

Q: Solve J²u = Ət² u (0, t) = u (x, 0) = J²u 4- 2 მ2 u (π, t) = 0 sin (2x), 0 0 (x, 0) = 0 Ju Ət

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Q: how that: (f)=X*(-f) x(t) is even, then b₁=0, an= To

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Q: du du dx' dy 1) u = 3x²y + xlny² - Inxy 2) u =xe*Y+ ‡ ArcTan , 3) u = +2²-3² I. Find and (whenever…

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Q: =/4 sin z 23)/" dr cosr

A: We’ll answer the first question since the exact one wasn’t specified. Please submit a new question…

Q: Show that given that z = sin-12 дхду дудх

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Q: The antiderivative of the function sin (Gx+7) is:

A: Given : sin12x+7

Q: Q2) A Differentiate the following ( 1)y= [(5x) (4- 2x)]²

A: As per bartleby guidelines we only give first question answers.

Q: 1/2 yee? +4 dy +17y=0 dx2 when Pove then ydy that Sinzx, %3D0 dx

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Q: | ( + a + a) sin(8r") + 9z²)dr. Let a be a constant. Evaluate Türkçe: a sabit bir sayı olsun. (2 +2…

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Q: 3. Prove the Distributive Laws: PV (q^r) = (pVq) ^ (pVr) and p^(qVr) = (p^q) v (p^r).

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Q: ху • prove that x +y Example If z = az dz + y.- Əx х. ду

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Q: Hico/ prove Thall Cosh2: - 2 tañ z Sinhz: 1+2 Tanhiz =

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

Q: B. Let ulr,e) = r"sin(ne). Find 4 2n-2 +u -nr Ure or

A: Given

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