Some body started at A(6, 0) and coordinate change by AX = -6 and AY : O Find its new position ? * %D (0,0) O (1,0) O (2,0)

Q: M. y dV, where E- {(x, y. 2) | 0 x* 3, 0 yx, - yEs+y}

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Q: Evaluate ff, x² In(y + 1) dA where R = [0,1] x [0,1].

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Q: у" — бу' + 9у %3 t'e", y(0) 3D 2, У (0) 3D 17

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Q: w = 4x + y² +2²³₁ x = ers²₁, y = 1 y = In(r+s).

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Q: The spread of a virus is modeled by V(t) = -t° +t² + 12t, where V(t) is the number of people (in…

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Q: Trapezoid JKLM is shown below. y 4 К (2, 3) L (4, 3) 1 (1 1) M(5 1) 3. 2.

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Q: 2. -1z"cosdz zl=1

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Q: dt t3 Vt? - 9 J3v2

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Q: (a) f(x,y) = (x² + 1)e" (b) g(w, z) = w? + 22 (c) h(x, y, z) = vT² + 3y – xyz²

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Q: xbe inner froduct x+y Lx_y ?

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Q: y = 8e*, on x e [0, 2]

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Q: I shift as in Example 4.9 to find the general solu b. (2D – 1)²y = 0 + czx?)e2x

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Q: // | *dædydzB = {(x, y, 2) =€ R® 0 <« < 1,0 < y < 1,0 < z < x} {(x, y, 2) =€ R° 0<æ < 1,0 < y < 1,0…

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Q: Differenitate: y = esin (z²+2z)

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Q: V1-y² -1 0 kpxpzp (,x + zA),I „«-,S

A: The given integral is: I=∫-11∫01-y2∫0x y2+x2 dz dx dy

Q: f(z, 9) = 82" + 5y² + 4z°y+ e7=y of Calculate

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Q: find dy/dx

A: Known formula: ddx∫rxqxftdt=fqx q'x-frx r'x.

Q: z· 3°dz

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Q: x = 2 + 3t, y = cosh 3t , 0 <y<1

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Q: (b) Hạ: u < HO,n = 30, t = 2.431 = 0.011 P-value %3D

A: Given : Ha : u &lt; uo  n = 30  t = 2.431

Q: 6z ry- (y² zi + j+k) -i do 6.

A: The surface is defined as, x2+y2=42z=1z=7 The plot is a circular quadrant as observed in the…

Q: dw ,s = 1 If w = 2x? ds + y, x = 2 - s, y = 1+ 2s², then by chain rule when %3D సా | 8

A: See the attachment

Q: 522 – 7z+3 dz - 12 dt 15w – 13u? + w dw f) e) d)

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Q: B (2x + 3y² +42³) dV, where B = {(x, y, z)|0 ≤ x ≤ 1,0 ≤ y ≤ 2,0 ≤ #≤ 3} 08 192 170

A: dv = dxdydz And put the limit of integration.

Q: 2+i Evaluate (2x+1+iy)dz along (1-i) to (2+i) 1-i

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Q: (i) Find the covariance of Y1 and Y2, Cy, Y,

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Q: 23 { , si (x, y) # (0,0) b) g(x, y) = 2x2 + y² , si (x, y) = (0, 0)

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Q: 5. By Chain Rule , evaluate b. y' for y = u² + 2u and u = x² + 2 %3D

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Q: Solve by Chain Rule 8 poir f(y) = /2y + (3y+ 4y²)³ %3D

A: Here clearly not mentioned, what to do with this question, but as we know chain rule is applied to…

Q: (ii) Assume that d = in E-coordinates and 7 in B-coordinates. y' Find a' and y' expressed in x and…

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Q: d K, d1 + d. +... + K, 2 n K, K, 1 n

A: Let d=d1+d2+....+dn From Cauchy Schwarz inequality , we have- d1k12+d2k22+.....+dnkn2…

Q: Calculate || xVy² + x²dA, Where R = {(x, y) /0 < y <land 0 < x < y}

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Q: lf f(z, y) = 5ery + 1 sín (inr + y) + 2r + 3y, find-a-,-,-and

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Q: If  z = 3x2 + y2  and  (x, y)  changes from  (1, 3)  to  (0.95, 2.9),  compare the values of Δz…

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Q: x, y) Edy is

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Q: 2 2xy) dy, v es (0, 0), (2, 0), (

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Q: a) Let y" + xy' + y = 0 be given. Why does the approach y(x) := e^× does not work?

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Q: Use Example 4 to calculate -(r x r'), where r(t) = {t, t2 , et)

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Q: - 6х + 2у, dt dy -3х + 1у dt

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Q: dz and Use the chain rule to find du for z = 4x?y3 – 2x² + 3y where x = uv and y = u –- v

A: Given, z=4x2y3-2x2+3ywherex=uv and y=u-v

Q: H = 2 = 0, n2 = 22 and n, 18, thus df is: %3D %3D

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Q: te² i· k) dt V1 – ? 40.

A: Solving by definite integral we have

Q: Q(x, y) = 42x1/5,A15 Where Q is the output in millions of units of product.

A: Given data:     The given output of the factory is: Q(x,y)=42x1/5y4/5. The sum of the amount spent…

Q: t) = y"+y= √2sin(√√√2t), y(0)=9, y'(0) = 0

A: Given,        y''+y=2sin2t, y(0)=9, y'(0)=0

Q: The colution oF y" + 16 y = 0 is y= C,cos 4x + C2 6in 4x. IF y C0) = 8 and y' (T/4) - 32, find…

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Q: 33) - 2y + y, + y; = 0, y + y', = 4t +2, y, (0) = y, (0) = y,(0) = 0 y + y, = t² +2

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Q: Find 2 by using the Chain Rule with y as a composite of dx y = csc(u), u = x3 + 2. %3D

A: Given: y=csc( u) , u=x3+2  To find dydx

Q: ='i+(2xz - y)j XZ and (2, 1, 3) is

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