3. If u= (x+y +z') , prove that +y

Q: az xdz + Y- = xy+z. a) If z = xy - xei , show that x- ду

A: Since you have posted multiple questions in this question which are not interlinked so I have solved…

Q: find in Euler's way 2x ! y(0.1) de y(0)=1 , h=0.05 y' = y -- y

A: The general form for Euler's method is given by yn=yn-1+hfxn-1,yn-1.

Q: 2. Let f(x, y, z) = In(x² + 2) + y²e#* - cos(2yz). Find fzyz-

A:

Q: 7 y=tanx show thats y" = -2Siny cosy 1f y=e Snbx show that:

A: Dear Student, according to the Bartleby guidelines, we can answer only first question if multiple…

Q: Find Oz! ôu and dzlôv for z= 4e" In(y), x In(u cos(v), y=u sin(v) at the point (u,v)= (2, 7 / 4).…

A: NOTE: Refresh your page if you can't see any equations. . take the partial derivative with respect…

Q: Prove 8xyz < (x + y)(y + z)(x + z) for every x, y, z E [0, +∞[.

A: We have to prove given identity: Concept:

Q: (2 dr z²–10z+15) Integrate:

A: NOTE: Refresh your page if you can't see any equations. . take long division

Q: Prove thiat dx Ś (areten()) ) = し 4+X

A:

Q: Prove that the derivativeo P(zx tJ's 4(2Xbjusiy Pirst Princiele 4(2X+)by jusing first Princiele…

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Q: /9 – 2° dz Integrate: z4

A:

Q: Use two different methods to calculate dzu/ar if u = /x² + y². = est, and y = 1 + s² cosz. IUse two…

A:

Q: Prove that u exy)= (x+a)Ly+b) is the exact Solution of the pOE Ux Uy = 4xy ucy) where (a) and (b)…

A:

Q: Q6:-Prove that: y" = 1 if y=;csc (tan"

A:

Q: Q4 If f(x, y) = In(x² + y² ) %3D Prove that dy2

A:

Q: x*y" + xy'+4y= 2x Ina

A: Cauchy linear differential equation

Q: 2² + e4 z lim z 0 22 – e²

A: This is a form of infinity by infinity so we have to apply Lhospital rule that is differentiate both…

Q: 2xy + In(8 + z²), x 7v2 ', y = 9u + 3v, z = cos(4u). Find dwlðv when u = 5, v = 2. Suppose w = ,X =…

A: We have, w=2xy+ln(8+z2) x=7v2u,y=9u+3v,z=cos(4u). Point (u, v)=(5, 2)   As we can see that x, y and…

Q: 4. Show that evx dx = 2Vxevx - 2ev + C Hint: Make a substitution first before doing integration by…

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Q: 1 prove that | e -ym dy = mr(m) -ут

A:

Q: iv) if zy = (x)- then zx + Zy = %3D %3D

A:

Q: In r dy If y , then is cosh z

A: Straightway proceed to differentiate both sides,

Q: 2. Show that the Euler-Cauchy Equation Iy" + axy + by = 0, 1+0 can be transformed into the constant…

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Q: Let Use Euler's Method with h=.5 ond (X,Y.) -(1,1) to estimate (a, y )

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Q: ==4-x² - y² for which z ≥ 0 with upw= rcle x² + y² = 4 that forms the boundar

A: The Stoke's theorem states that ∫CF·dr=∬S∇×F·dS Where z=gx,y and dS=-gx,-gy,1dxdy.

Q: 8 Evaluate the integral dx using the two-point Gaussian quadrature rule. 16+z1 -2

A:

Q: Suppose that z = xy² and x and y are differentiable func- tions of t with x =2,y = when t = -1. Then…

A:

Q: Use at least two methods to prove that dr/dt=0 when r=√x2 + y2, x=α cos t, and y=α sin t if α is a…

A: First method   r=x2+y2r=(α cost)2+α sint2            since x=α cost and y=α sint  =α2cos2t+α2sin2t…

Q: ==, j= 4 and x=0 about tue liney=5

A: Disk method: -  When the axis of revolution is the plane region's boundary and the cross-sectional…

Q: Are these equation separable 1.s2+ds/dt = (s+1)/st 2.dr= b(cosx dr+ rsinxdx) 3.y'=ye(x+y)/(x2+2)

A: The objective of the problem is to determine whether the given equations are separable. A…

Q: az az and as Use the chain rule to find at (=) Z = tan V u = 8s + 5t, v = 5s – 8t az as az at

A: Topic:- derivatives

Q: 2 2 If z = f(x, y), where x = s² - t² and y = t² s² and z is differentiable, then - Select one: True…

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Q: 1 Verify Eular's theorem for z=- =(x²+xy+y*)' x²+xy+y² 2

A: The expression z=1x2+xy+y2=x2+xy+y2-1. We have to verify the Euler's Theorem.

Q: 11. Prove that tanh y du = In cosh u + C

A: The integration of the integral is tanhu.

Q: 4. Let z = x2 + y³, x = 2st, y = s - t2, s = u", and t = u sin w. Compute for Oz ду and дw ди

A: Let z=x2+y3, x=2st, y=s-t2, s=uw, and t=u sin w.To compute for ∂z∂w and ∂y∂u.

Q: dy then In z is If y = cosh z

A: Without wasting any time, any further, differentiate the RHS to get your answer.

Q: (x) = 3x +12x+2, %3D ues of a, b and c such that

A:

Q: - seyi + avīj + () dt = 3 3

A: We have to perform integration by parts and then insert given limit

Q: Compute sec? z + x) dr

A: Given : ∫12sec2x + xdx

Q: dy 1. If (x + y)² = x² + y² prove that 11 I Alx y

A: As per rule of bartleby we can solve only one question at a time and we can solve only three subpart…

Q: Find y' if exy = e 4x -esy-

A: NOTE: Refresh your page if you can't see any equations. .

Q: B. Let z- ( x-y)e×y (x-y)exy Show: Zxx + zyy + exy Cya-x3)= -z (xy+ 2)

A: Partial derivative of a function z=f(x,y) with respect to x is the derivative of z keeping y…

Q: ) Fnl the Vdume of the Selid enclesed by the curres "about the x-axS. y=e^, y=0 x =©,'x=/

A: To find out the volume of solid of revolution.

Q: Q1 : prove 1 2(1–z) 3(1--z) dydxdz = 1

A:

Q: 2 dt 22. Evaluate o v9– 2t² 2 dy 3-y³ 24. Evaluate o v8-y'

A: 22)I=∫0129-2t2dtt=32 udt=32 duI=∫29-9u2 32duI=2 ∫11-u2 duI=2 sin-1uI=2 sin-12 t301I=2 sin-1(23)

Q: Suppose that x2 = y2 = e and yz = zxy. Show that xy =yx.

A: Since, yz = zxy

Q: 7) [[3embch5y] dvl [jel*5) dy] „In[sec h 5y]

A: Using rule of logarithm &amp; integration formula of sech(x)

Q: 4. Prove 1 < | V1+ a dx <2 0,

A:

Q: 12- show that x² J.(x)dx = x²J1(x) + x J,(x) – lo(x)dx

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Q: 4. Prove that ах x" ea" dx xn- п-1 ‚ax dx а а

A:

Q: Verify Young's Theorem z = In(2x + y) y? x2 +e(x+2y) y

A:

Domain

In simple mathematics terms, a domain is defined as the space on which all the possible inputs for the function will lie. It can also be expressed as a set of departures for the required function.