+ y²) dæ – x (a² – y²) dy = 0 r (x2 - y? dr + (x2 + 3ry + 4y) dy = 0

Q: %3D %3D dz Find at (2, -2, 1) if x + y? +z2 = 6xz+6yz+21 = 5 =D1

A: Given equation : x2+y2+z2=6xz+6yz+21

Q: 2x Ex FIND THE DERIVATI VES %3D

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Q: function fo) = 7X1+10x10x3_4 Qn Antiderivative of fo) is F(x) = Axn+ Bxm, CxP+Dx: A= 710 %3D where…

A: Solve the following

Q: Find where 1)let . V°g r = l7| -- g(r) = In(r³) s = xi + yj + zk * vo x Vp 2) find = yz + zx2, P =…

A: Gradient and cross product

Q: ven f(x,y) = -2xy² where x = 5t and y = 8t2. Findf' (t) at t = 3. %3D

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Q: dy Let y = (x2 – vx)4". Find using any method. dx -

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Q: Q) Find y" + 3y 5y at x-5 where y = xsin(1/cscx))

A: NOTE- AS THE SECOND QUESTION PICTURE IS NOT CLEAR SO I AHVE DONE ONLY FIRST QUESTION. IF YOU WANT…

Q: Integrate the following using substitution. You must show work. 7y(v² + 7)°dy

A: We have to find the definite integral using substitution method In place y^2 =t                2y dy…

Q: 15. f(x, y) = xy /x² + y V9 – x² – y? 16. f(x, y) ▪ x + 2y + y? x² – y? 17. f(x, y) *

A: 1.  fx,y=xyx2+y2.  fx,y=9-x2-y2x+2y3.  fx,y=x2+y2x2-y2

Q: D = {(x, y) E R² :0<x <∞, 0 < y<∞} olmak üzere, [ rye--v°dA D.

A: A multivariable function f(x,y) is a rule that is used to associate a number or quantity with a…

Q: Q4) Find y" + 3y' 5y at x=5 where y = xsin(1/cscx))

A: Solution:-

Q: 2.rydr + (z² – 1) dy = 0 O zy? - y = C O zy+y=C O zy - y² + C = 0 Oy-

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Q: F = [r. -x, 0]. = [y. -X, S: 3r + 2y + := 6, x2 0, v 2 0, z 2 0

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Q: 2. [f 5y ey dA, F- {(x, y): 0 s x s y?, 0 s ys 2} F

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Q: Q3) Find aw dw & ar ds interms of r&s if w = x+2y +z x= y = 4r2 + In 2s & z = 4r X=- %3D

A: Given: w=x+2y+z2, x=rs, y=4r2+ln2s &amp; z=4r. To find: ∂w∂r and ∂w∂s. Solution: Partial derivative…

Q: 4 J4- y ktx dy S[S( x, y) dA = [] 3 R 0 2- 2 2

A: Consider the given expression, ∬Rfx,ydA=∫04∫2-y24-yx2-x33dxdy This suggests that the region spans…

Q: d²y Given that x3 + y³ = 2, prove that 4х %3D dx2 y5

A: Given problem:-

Q: z'z + yz? + 2xy? – 2³ = 0 ve z = f (x, y) ise =? what is the at f(0,1) O a. 0 O b. 2 О с. 1 O d. -1…

A: Find the partial derivative of z with respect to x

Q: (c) Ã = xẽ, + yếy, C : {n² + y² = 1, z = 0} %3| ex (d) Ā = En + Ey 2 + 12 C : {y = x, z = 0, x € (0,…

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Q: af af a²f 1. Given f(x, y) = x' + y* find ax ' dy' dxdy and - дудх

A: Please see the answer below

Q: se Green's Theorem to evaluate SC (5y-9x)dy-(yx-x³)dx where C is shown below

A: Follow the procedure given below.

Q: What is P,(y) if the given DE is xydx – (3y – x²)dy = 0? Select the correct response: y 2y O -2y O…

A: Topic:- non exact differential equations

Q: . If U = z sin y/x where x= 3r2 + 2s, y= 4r – 2s², z = 2r? – 3s², find a) Or b)

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Q: Q3. Find af and at se If f (x, y) = 2e* + Iny2 ,and x = 2t + r2, y = ar r+1

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Q: d²y Given that x3 + y³ = 2, prove that 4x dx² y5

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Q: dx using miscellaneous substitution will yield to secx + 1 Transforming S Ⓒ √ ²² +²2 dz (Α) -z²…

A: This question can be solved by substituting z=tanx2

Q: (2 fi = f(x²+xyz, y² +22= Prove that (y²-2x) ou 2ZX) then ne (²h-x) he 18

A: Concept: Partial derivative : The partial derivative is similar to the normal derivative except in…

Q: c3 Q3/ Evaluate , S(6x³ + 6y²) dx dy using Simpson's 1/3 rule in x-axis and Trapizodal rule in y…

A: Given ∫23∫466x3+6y2dxdy

Q: 5Is there a value of r sotha X = 1 y = 2 and Z=r is asolution to the linear systen ? If there is ,…

A: Putting equations as;23-11-1241-2 xyz=11-712Augmented…

Q: What is the general solution of (D² – 2D + 5) y = 0 ? - y = Cie + C2e3 %3D y = Cie cos 2x + C2e sin…

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Q: (b) / / | /3(x² + y²)dV, where V is bounded by y = 2r² + 2:² and y = 8.

A: The given question seems to be incorrect. The function inside the given square root should be…

Q: Given Yy - y = – ỹ Yy - y + y. - ỹ and (y — У )? [(Yj – J,) + ỹ, – ỹ )]² 2. %3D

A: Given that

Q: 2. 2sin(хy) at x D 2, у3D Зя/4 3. z= In(x + 1) + y° at the point (0,3,9)

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Q: س/ أختار قيمة R ,D المناسبة ل لداله الاتية f(x) = 2 + Vx? - 1 Df = {x:xeR:x 0} O الخيار رقم 1 D, =…

A: The given function is fx=2+x2-1. Calculate the domain and range. Range is defined the all possible…

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: Q4) Find y" + 3y' 5y at x-5 where y = xsin(1/cscx))

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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: -0.08. Then evaluate dy for a=-3 and dz *+1 %3D Let y = dy = %3D

A: We have to find

Q: dy Va2-x2 with initial condition y(a) = 0. dx -a va2-t2 dt This can be solved by y = J %3D II

A: From the above question, we get the differential equation dydx=-a2-x2x with the initial condition…

Q: √√√(-) True f(x,y) dx dy False - L.T. 1.². f(x, y) dy dr

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Q: find 04 O B O 7 O -12 af ду dy' given f (x, y) = e + 2xy² – 4y at (0, 3) -

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Q: if y' - y =2x Then, d'y -24y prove that dx (3y –1)

A: Given that: y3-y=2x

Q: f f Find Af = where f(r, y) = In (9r2 + 5y2 – 3r). %3D

A: Here f is two variable function .To find ∆f , first calculate fxx and fyy then add them.To find fxx…

Q: 2: find fr, fy, and fz. 9 f(x, y, z) = 1 + xy? - 222 5 f(x, y, z) = x - Vy² + z?

A: (a) Given f(x, y, z) = 1 + xy2 - 2z2 So fx = ddx(1 + xy2 - 2z2)    = ddx(1) + ddx(xy2) - ddx(2z2)…

Q: sin(r. r dr dy. Compute O y/3

A: To evaluate∫01∫y131sin(πx2)x2 dx dyx= y13y = x3

Q: Q2: Given y = f (u) and u g(x), find dy/dx: y = 2u3, и %3D 8х — 1

A: Differentiate

Q: 16. f(x, y, 2) = y - Vr? + z?; P(-3, 1, 4); a 2i-2j-k

A: To find the directional derivative of f at P in teh direction of a So, given f(x,y,z)=y-√(x²+z²);…

Q: + yz? + 2ry² - 23 0 ve z = f (r, y) ise =? what is the at f(0,1) %3D %3D O a. 2 O b. -1 O c. 1 O d.…

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