Let D- Evaluate z dv.

Q: 10. If z = x + f(u), where u = xy, show that dz = x. х дх

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Q: Find fx, fy and f z if f(x, y, z) = e*yz In zx. %3D

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Q: Let f(x, y) = xcosy- y e*y. fry at (1,0)is equal to: -5 3 -1

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Q: If z = In(x² – 2y), and x=u+v, y= e" , find and du If w=2xy'z', and y =x² +1, z= Vx, find dx

A:

Q: Suppose f(x, y, z) =

A: Given,            f(x, y, z)=1x2+y2+z2 and W is the bottom half of a sphere of radius 6.

Q: aw Find ду if w = z³(In(zy))(e**y*z*) %3D

A: Given,        w=z3ln(zy)ex2y3z4

Q: Evaluate the followingintegrals.∫(z+1)√(3z+2)dz

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Q: Evaluate 2æz dV where E = {(x, y, 2) | 2 < * < 3, z < y < 2x, 0 < z< z + 2y}

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Q: If e dy then y-

A: We will evaluate the following Integral.

Q: Use Green Theorem to Evaluate yx'dx – x*dy where C is left half of x² + y = 25 77.7704 O 78.7712 O…

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Q: Compute f, aL a2f and :f(x, y) = (x + y)(2x + y)² ax' ay дхду

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Q: now if we take F (x, y) = (ax, ay), where a is any positive constan %3D

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Q: Prove that fdr = [[ dS×Vf %3D

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

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Q: dv av and ду ди ди 2. suppose f(z) = u(x,y) + iv(x, y), show that əx %3D ду əx ||

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Q: Let D-{tx.y.2) : 2+y?s2s 1, z2 o}. Evaluate z dv.

A:

Q: If FGx) = -2x+s firid f(z)

A: Given: if f(x)=-2x+54To find: f(1)

Q: dy let y = xtan z then is da elect

A:

Q: Evaluate the integral. e3t V2 + et dt =

A: We have to find the indefinite integral

Q: . Show that z)= E kz is D: 1215 continuous io domain

A: The series can be shown as continuous in a domain if it converges. Therefore, the first calculate…

Q: Evaluate the integral. dt V 4 + t2

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Q: Evaluate S, y dv with E = {(x, y,z): 0 <x< 3, 0< y < x, (x – y) < z < (x + y)} %3D

A: Use triple integration

Q: 2 calculate J= e dyok 2x

A: Given integral :

Q: dy 3. Find dæ if y = In (aVæ +1).

A: Given,            y=lnx3x+1

Q: im(z,v) →(0,0) F(x, y).

A:

Q: If u= In x, then 1- (In x)2 dx=?

A: Find your answer below

Q: If dx = In |x| +C, then d 및 (In |x| + C) = for x> 0. X

A: Given,         Assuming that x&gt;0, use differentiation to justify the formula ∫1xdx=lnx+C.…

Q: 10. If z = x + f(u), where u = xy, show that дz dz х дх = x. ду

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Q: Compute the given fac re dx %3D

A:

Q: Expand (x − y)(z + w − t)

A: Expand (x − y)(z + w − t)

Q: prove that 16 x (I+x) dx 306

A: The product rule of integration states that∫fxgxdx=fx∫gxdx-∫f'x∫gxdxdx.

Q: Evaluate the integral.

A: To evaluate: ∫221t3t2-1dt Let substitute u=t2-1 dudt=12t2-1·2tdudt=tt2-1dt=t2-1tdu Limit will also…

Q: (4) Evaluate : S[(xy? + yz') dV if Q = {(x, y,z): x:[-1, 1], y:[3, 4], z:[0, 21}

A: Note: As per our company guidelines we are supposed to answer only one question at a time. Kindly…

Q: Let z = 3x*y, find Vz.

A:

Q: Suppose Vf(x, y, z) = 2xyzexi + zex¯j + yex k. If f(0, 0, 0) = 1, find f(1, 3, 3). ,2 .2

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Q: fx'e*dx

A:

Q: fx'e* dx ets

A: To evaluate:                     ∫x2 ex3 dx

Q: If u In x, then 1-(In x)2 dx =?

A:

Q: Given that z = f (u,v), u=x + y and v = 2x - 2y. Show that 4. дхду ди?

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Q: if y ". y (In z) (a) Find

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Q: If z = f(x, y), where x = 2ts and y = t2 + s², show that () - 2 + 2x + 4y %3D dsdt

A: Here given z=fx, y and x=2st, y=s2+t2

Q: If X is a RV with f(x) = 0, when x 0, P(X 2 a) <u/a. %3D

A:

Q: Let D={ (x, : x2+y2+z²< 1600, z2 Evaluate z dv.

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Q: . If z = f (x, y), where x = e" - e and y = e - e", show that TM UT az x: az az az dy ax UTM UTM UTM…

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Q: Calculate az/ax, where xez + zeY = x + y.

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Q: Q/ z = x + f(a) and a = ry. Show that: 尝-端=

A: We use the definition of partial derivatives to prove the given result.

Q: f(z) =z? is discontinuous

A: f(z)= z2 is a polynomial function in z and polynomials are continuous everywhere.

Q: Evaluate z cosz dz where C is (1)|z – 1| = 1 (i)피 = 2

A: Answer

Q: If dr/dt= -r5, what is r(t)?

A: Given drdt=-r5. The we have to find r(t) = ?