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Q: If  x2 + y2 = z2, find dy/dt when x = 3, y = 4, dx/dt = 6, and dz/dt = 2.  (Enter your answers as a…

A: Solution: the objective is to find dy/dt

Q: 10. dr S f(æ) dx = Choose...

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Q: 2 al S ex+y dydx

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Q: 3 (D² + 4)y = Ost<3 3t +2 t23 y(0)=0, y'(0)=1 Find L{y} L{y} = 1 3 3e-3s 8e-3s $2+4 s(s² +4) 2…

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Q: 2. given that y = 0 at r=1

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Q: 2. Compute F-dr where E= (x+ y,x-2z,z- y) and curve C is the line segment from (-3,5,1) C to…

A: Using line segment as the base of a rectangle, we choose the height to be the height of the surface…

Q: In Exercises 13–24, draw a dependency diagram and write a Chain Rule formula for each derivative.

A: Since, you have asked multiple questions, we will solve the first three for you. If you want any…

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: f(x, y, z) = eVx2 + y2, E = {(x, y, z) | 1 < x² + y2 < 4, ys 0, x < y/3, 3 s z 5 4} E = {(x, y, z) |…

A: given fx,y,z=ex2+y2 and a region of integration E=x,y,z|1≤x2+y2≤4 , y≤0, x≤y3 , 3≤z≤4 claim-…

Q: dy If y = e8z+13 then- dx O 7e8z+13 O 13e8z+13 O 9e8z+13 O 8e8z+13 O 104e8z+13

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Q: 2Use divectional devivative delinihion of f(Hiy)=x y'at the divecionof ū =i jatthe Point (le2>

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

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Q: 4. xy²1₁ X=1, x = 4, y = 0; about the x-axis

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Q: 8 (6562) 243 를-), then xo = If the length of the curve y = 3 x7 from the point (0, 0) to the point…

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Q: 4- Find Y/dz If x²(x- y)? = x² - y? dyla

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Q: ー28- Sa Oclumina f dz sabishy cauchy- Reimon quakir f andlgove @ frz= J-2xy ti C-Xyz] +z* @ f(2)=…

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Q: 2/3 Determine the length of x=| for 0<ys2. Assume that y is positive.

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Q: B. Let z- ( x-y)exy Show: Zxx + zyy + e x9 Cy 3- x³)- -z (xy+ 2)

A: Given that                       z=(x-y)exy

Q: 2- Max z =30 x, + 30 x2 X +2 x2 2 80, 3x +2x2 2 120, Simppler s.t. X, X, 20

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Q: What is G = xy ax – x²y ay + 2y az at B(3, –4, 1), expressed in SCS?

A: Given: G→=xy ax-x2y ay+2y az -----------(1) Where, Bx,y,z=B3,-4,1 --------(2)

Q: cancer u alcurate 5th on diagnostic test is 9s 2 those who halse A 'cancer cnd on those wno do not

A: Given that, As the test is 95% accurate for both who have cancer and who don’t, therefore the…

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: Sm Vx dx

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Q: 2. Find the linearization of the function f(x, y) = In(x³y®) at the point (xo, yo) (4, 3). Leave all…

A: Consider the following function: fx,y=lnx3y6 fxx,y=ddxlnx3y6=1x3y6×3x2y6=3x…

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: Determine the value of the Wronskian W (y1, Y2) of y" – 2y +1 = e2 (x +1) if x=1.3 by using…

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Q: 3. If z = f (x, y), where x = e“ – e® and y = e® – e", show that UTM UTM az az UTM X : az - ду dx…

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Q: If fufe.- fuave diffa Veubable at'xo eI fuave difle Veubable at Xo eI Pi:I R,ists-n prove O…

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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: In Exercises 5–12, find and sketch the domain for each function

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Q: of fxyl = 3X-y+6 Subjected QI Find to x+y=4 extrume v alues

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Q: 2.4. Compute and plot y[n] = x[n] * h[n], where %23 1, 3 s n < 8 0, otherwise x[n] = 1. 4 s ns 15…

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Q: 2): Consider the DE y" – y" – 6y = 0 -

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Q: Thene m for Voritly functiom Mean Valne fex) 2. 3X -4 +S the

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Q: H.W. a PDE from the followi'ng- @u=f() Form メツ 0u=fcx?ー)

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Q: B/let Flx)=[X]-X,x E(-2,2).which valuesof x o E(X) continuaus?

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Q: . If 4=(x+2y+az, bx-3y-z,4x+cy+22) is irrotational. Find constant a,b,

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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: 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: dy dx If y=e+19 then O 19e+19 O 4er+19 O 57er+19 O 3er+19 2er+19

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Q: 10- If f(u, v, w) is differentiable and u = x - y, v = y - z, and w = z - x, show that fe fe fe = 0.…

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Q: EX~U(0,1) if Y= =L l(t-x)~ Exporential (A,

A: From the given information, X~U0,1 The probability density function for X is, f(x)=11-0       =1,…

Q: Ôz 12. If z = cos(x y)+ y cos x , where x=u +v and y=u-v use the chain rule to find and ди

A: Given: z=cosxy+ycosxx=u2+vy=u-v2 Recall the chain rule,  ∂z∂u=∂z∂x·∂x∂u+∂z∂y·∂y∂u…

Q: Find y' if y= In coshv tanh v. y =sech v-2tanh v O None of the above O Option 4 y=tanh'y y'=tanhv –…

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Q: 3. Find general Golution y" + y= Secx

A: Given that, find the general solution y''+y=sec3x (D2 +1)y=sec3x

Q: Find dr. J (1+z²)3/2 - In Vx² + 1 + x| + In |Vx² + 1 + x| - Ja? + 1 +c Vx² + 1 O Option 3 Option 1…

A: Let I= ∫x21+x232dx Let x=tanθ ⇒dx = sec2θdθ Substituting this in I, we get

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

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Q: Suppose z = 2xy where x = t^2 + 1 and y = 3 - t. Use the chain rule to determine which of the…

A: In the given question the functions are given as z=2xy , x=t2+1 , y=3-t . The objective is to find…

Q: 16.1. Use an antiderivative to show that for every extending from a point 21 to a point 22 2" dz =…

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