Find dz ди Z = fan ( auf dz av as fn. of u and if ),X = u Cos V, y = usinv? (y)

Q: Compute the work done by the force 7 = (sin(x + y), xy, x²z) in moving an object along the…

A: Given force The object is moving along the straight line and from

Q: Find order and degree of y'+ (y")? =(x+y")? O a. 2,1 O b. 1,2 О с. 1,1 O d. 2 ,2

A: The given differential equation is                                              y'+(y'')2=(x+y'')2…

Q: Q2/ find dz ond dZ as function ne U and v if of Z=tan (중), X=u Cos V , 9-u sinV

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Q: Iffis of class c? and z= f(y.x), con u= x°y°,v = 5x+1. Verify that| :4xy kxy+ 4x³y° + 10xy- af дхду…

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Q: The Anctien fay 'and i not depned frather veher stake the demanin of sec d h....... the invens…

A: Given that f(x) = sec (x) ; 0<=x<pi/2. we have to find the domain of f-1(x). and we have to…

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

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Q: 5. y-2y+y-6e* d'y dy 6. 2. dx2 +2y e2x d'y dy 7. 2 -2y D4e 3x *

A: 5. givend2y(x)dx2-2dy(x)dx+y(x)=6exThe general solution will be the sum of the complementary…

Q: S cos“ xdx = sinxcos² x + sinæ + c Select one: O True O False

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Q: Which of the following is not true? Select one: d [uv] = uu' + vd dx O d [uv] = u · + v • u' dx v -…

A: topic - derivative rules

Q: 2. Show that the function u p(ry) + Vry v(y/x) provides the equation Pu = 0. ду? dx²

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Q: of Then x y

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Q: əz Use Chain Rule to determine and where

A: We have to use chain rule step by step.

Q: у У1 Уз Уч У 4 | Уб 6 У 7 У 7 64 If y = cos ax, prove that У 2 5 = 0, where y, Ув 8 = dr ту. dx'…

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Q: Show that a fuinction F:R>R defired by 3 If I=y=0 1S continous ert (o0)

A: Continuity: Let a function f(x,y) be defined on an open disk B containing the point (x0, y0). A…

Q: Jige If f(2) =-3, g(2) =4, f' (2) =2, and g' (2) =, d. then dx -21 16 9. 16 -13 16 29 16 6 jp 3…

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Q: If w= f(x, y, z). Use implicit derivation to find w² + w sin(xyz) = 1 ? Ow дх Iw Ow for the…

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Q: Find the first 3 Zerms o Sinx et a =?

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Q: dw и and if w = x³ + In (²) dv E) + y, x = u² –" + 5 and Find - ди y = 3v + 5u and point…

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Q: Find dy/dr. y = In(re")

A: Given To find Derivative of y= ln(xex)

Q: Let g(s,t) = As" - cost, cost -s"), which of the following is true? O A. -sint- + 11s10. O B. 11s10…

A: given g(s,t)=f(s11-cost,cost-s11)x=s11-cost,  y=cost-s11differentiate partially g w.r.to s and…

Q: ut (X, Tof) be the cofinita to p. Jet A = {1,3]. etス=R B= Co1) %3D Fnd Ā ļ B.

A: Here given that X=R  Let A={1,3} and B=(0,1)

Q: For the function of two variables defined by f(u, v) = u cos v + v² sin u, select the option that…

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Q: find the dy さ× when 3In X リ=(メ+z)m

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Q: dx 7. = cosx cos² t dt

A: 7). To solve the differential equation: dxdt=cosx cos2t Solution: Re-arranging the given…

Q: fz=f(x, y), where x = e" cos v, y = e" sin v. Show that af af +y ду ди X = e2uf ду

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Q: f(x.y) = x³y – . Calculate Se af and əx ду

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Q: for 3x'z -x'y² +2z + 3xy = 0 ( Hint: Let %3D F(x,y,z) = 3x z - x'y? + 2z +3xy) %3D

A: Explanation of the answer is as follows

Q: 8. What is the derivative of y= Vu in terms of x? dy a) 2/y dulas b) 2vu d) 2/u

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Q: 64 If y = cos ax, prove that У У1 У г Уз У4 У5 |=0, where y Уб У7 Ув d' dx' у.

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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: Show that (∂z/∂x)2 + (∂z/∂y)2 = (∂z/∂r)2 + (1/r2) (∂z/∂θ)2

A: The equation to be proved is,