12. Prove: ΔUΧΖ-Δ AUXZ AYVZ ~ Z.

Q: 4. Show that z = a' Zax if z = e-al cos(x-at) %3D

A:

Q: az xdz + Y- = xy+z. a) If z = xy - xei , show that x- ду

A: Since you have posted multiple questions in this question which are not interlinked so I have solved…

Q: 1. Show that c(t) = (e¬t cos t, e-t sin t), 0 <t <∞ has finite length and calculate its valu

A:

Q: If =x+3y-z,=4xyz, w=22 -xy evabuate d(u, v,w)/ (, 2). at (1-,0).

A: We have to first find all partial derivatives.

Q: 12 3. If u lx + my, v = mx-ly, show that ди 4 + m

A:

Q: Evaluate: S (In(2æ – 1) – (5) + 25 ) dx - Limits: [1, 6] Using Trapezoidal, n = 30

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Q: 5.Use thelefinition to Rrave that Jw wh- 2

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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: Suppose w = 6xy + In(4 + z²) , x = - , Y 3u + 9v, z = cos(8u). Find dw/dv when u = -5, v = -6. dv…

A: *to find:- Partial derivative of w with respect to v, when u = -5 &amp; v = -6

Q: /9 – 2° dz Integrate: z4

A:

Q: 13. the , xydA, where ySxsy?}

A: First I have set the limiting double integral from given information and then solved it .Final…

Q: -2+z) ds over t e point (0, 0, 0)

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Q: xy If z show that: x- y

A:

Q: 1 prove that | e -ym dy = mr(m) -ут

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Q: 2. Show that e*, sin x, cos x are linearly independent using Wronskian Method.

A: As per the policy of bartleby the provisions is to solve only one question at a time  I am solving…

Q: Suppose that (Q x Q, +,.) is a ficld where (x, y) + (z,w) (x+z,y + w) and (x, y). (z, w) (xz +2yw,…

A: I have find identity of the field and then inverse

Q: 2) Eliminate the arbitrary enstant, 4 y= x*+ Cix + Cz e-X

A: Given problem:- Eliminate the arbitrary constants. of y= x² + C₁x + C₂ e-x

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A:

Q: Find y,(x) if y = In(In(Inx)).

A:

Q: To/t Integrate Ua ko To 3. Uz kg 2. eT-1

A:

Q: 1. Show that sinz is unbounded on C and lyl <|sinz] <ebl z=x+yi € C. for

A: Given:         We have to show that sinz is unbounded in ℂ and y≤sinz≤ey   for z=x+yi ∈ℂ Function…

Q: The Wronskian of y,(t)=e 2, y,()=e" is-e St. Select one: True False

A:

Q: 10. Given: YX = ZX WX bisects ZYXZ Prove: AWYX AWZX

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Q: 6. Given: AUVW = AXYZ Prove: UV || XY .Y W

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

A:

Q: 1. Use a Chain rule to find aw and ar aw , if w = x², x = sin(r²s) əs %3D

A: Given w = x2x = sin(r2s)

Q: Find the of im < Re z< £ un der w-

A: Substitute w=u+iv and z=x+iy in the transformation. w=1zu+iv=1x+iyu+iv=x-iyx+iy.1x-iyu+iv=x-iyx2+y2…

Q: Obtain the general soluti d²y 1. 7- y = 10sin²x

A: Given: d2ydx2-y=10 sin2(x)

Q: Show that if AT Ay = y for all y in Rn , then ATA = In .

A: Given that     ATAy=y  ∀y∈Rn. To prove ATA=In

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: 9 Give with an not example of T: W≤X →Y, to XT Ext. .R. boundedag. - keše bes

A: Please find the solution innext step this is an non-example of Tietze extension theorem in Topology.

Q: 3- prove that w comport dx =w dy yx 23 34 if w=: w = xy² + x³y² + x³y

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Q: dy then In z is If y = cosh z

A: Without wasting any time, any further, differentiate the RHS to get your answer.

Q: 1. If x, y, z E R, prove that (a) \x+y\ < \x| + \yl- (b) |x– y| < |x – z|+|z– y|, and (c) ||지| -…

A: Since you have posted a question with multiple sub-parts, we will solve the first three subparts for…

Q: If (x* – y*,x – z°) = 0,z = z(x, y), prove: az y3 az +x³z4 ax - %3D ду 3

A:

Q: b) Verify uxy = Uyx , if u = In /x² + y² . %3D %3D

A: Consider the given function. u=lnx2+y2 To verify the equation, find the derivative first with…

Q: 13- dy + 2xy = y diferansiyel denkleminin genel çözümü aşağıdakilerden hangisidir? -x* +c1 y = e a)…

A:

Q: Integrate the fuackion f=g regian bonndel by y the en6* y-o ver

A: The function is fx=xyThe region is bounded by y=x, y=6-x, y=0

Q: 5. Show that xZx + yZry = yezy if z= xy + y In xy

A:

Q: ) Fnl the Vdume of the Selid enclesed by the curres "about the x-axS. y=e^, y=0 x =©,'x=/

A: To find out the volume of solid of revolution.

Q: If w=xsiny +ysinx +xy then prove that wxy=wyx

A: The given equation is w=xsiny +ysinx +xy......... (1)

Q: = 1, prove that 1. If a + u bě+ u Ć +U %3D ди ду du ди du - 2| х +y Əz

A:

Q: Find the discontinnity point of &Cz): ニ そzそ+

A: Given that, the function is fz=z+1z2+2z+1. Set z2+2z+1=0 to find the undefined points. Compare the…

Q: 3,4 show that the integsal (Xy°ty%dx + 3) Independent of the path joining the peints (1,2)and 3,4).…

A: A function F is path independent if it is conservative. And if a function F is conservative then…

Q: Show that if AT Ay = y for all y in Rn, then AT A = In.

A:

Q: Show that Z/mnZ is isomphoric to (Z/mZ)×(Z/nZ) where gcd(m,n) = 1

A: Concept Used:( The First Isomorphism Theorem) If ϕ be the  ring homomorphism from G to G then…

Q: Suppose that the true model is () E+ and that it satishes MR1-MR6, but you estimate by OLS (II) W=…

A: From the given information, I yi=γxi+ei The OLS estimator of γ is, γ^=∑i=1Nxiyi∑i=1Nxi2 II…

Q: Show that lm Casy -1 CoSy-1

A:

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

A: