3-Evaluate Fdr where 2X Cisgiven by rit) = t3+U-3t)rék

Q: Evaluate | Vtan a sec" zdx. O a. 2 z tani z +tani +C 2 O b. 2 tani æ + tan +C 2 Ос. 2 O c. 2 2 t…

A: To evaluate the integral,  ∫tanxsec4xdx Rewrite the term sec4x=sec2x·sec2x…

Q: If --kr, show that d? dr %3D dt

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Q: Evaluate (2z + z – i) dz J|z-il=1

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Q: Let xe c and ye show that <xiy= y AX is qu inmer product if A is hermition positive del iniite

A: (Solving the only one question as per our guidelines) Question: Let x∈ℂm and y∈ℂm Show that x,y=y*Ax…

Q: Let z 2ev Then: 8z 8z dy sissis

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Q: evaluate the in! integ ral if u = 16+ ex then e* V T6tex dx = ( Jü cu=(ile %3D

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Q: Prove that c(u × v) = cu × v = u × cv.

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Q: 32. In APQR, mZP = 53°, PQ = 16, and QR = 10. Find m2Q. %3D %3D %3D 32. In AJKL, mZL = 113°, JK =…

A: 32. Here, we have given the length of two sides and measure of one angle of △PQR. So we will use the…

Q: Prove VZEC, V2|z|>|Re z| +|Im z| + |Im z| Vze C,

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Q: Assume X, Y CU. Prove that (U \ X) U (U \ Y) = U \ (X n Y)

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Q: 7. Show for y = u.v that y"= uv"' + 3u' v'" + 3u" v' + u''' v.

A: The detailed solution is as follows below:

Q: Use De moivres theorem to determine (3-4))"C4cis 30° )ieave your answer in 10 CiS the Formof Fciso

A: According to the given information it is required to determine the value of

Q: Oa Consy der he irlokonA Pram domain I 4.5.67 bo Codomaa row on oiraw DDiosiom brocelo kon A. ) is…

A: Definition: A function from set A to B is a relation in which every point in domain has unique image…

Q: Complete the proof that AUVX ATWX. U V T. W

A: Given:  WX=VX and UX=TX. In △UVX and △TWX WX=VX                  (Given) UX=TX…

Q: Let Z, = 2 cis 30° Z2 = 3elli %3D Z = In (1 + i) If Z = Z,Z, +Z3 Find IZ.

A: First we convert all expression into a+ib form then make necessary calculation.

Q: 4\ let ü = 31 – 2j – k, v = -i +j-k, w=41-2j + 3k And find u x (vx w) ?

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Q: What is u × w, assuming that w × u = 〈2, 2, 1〉?

A: Given,w×u=2,2,1 To find:u×w Solution: We know ,by property of cross product of two vectors (say,a…

Q: Show and use d(Xn, FCN))<« d(Xn-1 'x) Vny? To prove X = fx) %3D

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Q: DE : -t de dyx= 3et dt with indial conditins : xl0)=6 yl0)=1

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Q: mple. Compute AB and BA where 1 -1 A = %3D B = -2 2 3 4

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Q: Verify that the conclusion of Clairaut's theorem holds, that is, u, Uxy = "yx' u = x'y8 – y? With u…

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Q: If b is dviisible by a (a|b) and b in different than 0 then |a| is less or equal than |b|

A: The given statement means the following.

Q: Complete a two-column proof. Given: ZRSU VST Prove: ZRSV LUST

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Q: Let w = -4xy – 5yz – 4xz, x = st, y = et, z = t Compute (3,4) = as (3,4)%3D at

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Q: Consider a dihedral groop Dy=<agb: asb= (abj=1 Ds cuss all Dy and verify Subgooups of "Dy=…

A: See answer below.

Q: et A be 4X4r nas non-brivial . -son-

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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: Define the det product ICl=C_ d s à and B, which ane glven as A=An T'+ Ay+ Az and B Bx?+ By BzP in…

A: Hello. Since your question has multiple parts, we will solve first question for you. If you want…

Q: Prove that f, uv v • dỉ = – §̟ vũu • dĩ

A: Whenever the force is conservative in nature the work done over the closed loop is always zero. i.e…

Q: In R', the point (1, 1, 1) does not belong to the cylinder x + y = 2. Select one: True O False

A: Given problem:- In R³, the point (1, 1, 1) does not belong to the cylinder x² + y² = 2.  True  False

Q: 63. r(и, v) %3D Зи сos vi + Зи sin vj + 18u'k ||

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Q: Assume that u = U (x,y) iu differentiible and x =r ca Ô and y=rsin o eapress 2. entinely in termv 0…

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Q: Express E: livenr coumbination of Ÿ; = and V as a

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Q: Utu = c²uxx , u(0, t) = 0, u(1, t) = 0, u(x,0) = 0 U¿(x,0) = x² – 2x, 00 t> 0 t > 0 0sx<1.

A: Given P.D.E

Q: Verify that the conclusion of Clairaut's theorem is valid, that is, that uxy = uyx u = x4y3 - y4…

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Q: In the integration of (csc 5t)(cot 5t) dt, what is the correct "u"? O (csc 5t)(cot 5t) O csc 5t O…

A: I=∫csc5tcot5t dt Let 5t=u ⇒d(5t)=du⇒5 dt=du⇒dt=du5

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: Proue that || A|1maπi <j <n 1 Σajl . m

A: In the given question we have to prove that   A1 = max1≤j≤n{∑i=1maij}                         (1)the…

Q: find he querage vallwe of he fanction z-cor ox m De mternal ( )

A: fx=x-cos26x,   0, π6.

Q: Let V, 3 V3 = Vz= -3 8. %3D 131 2- -5 does { Vi,UeiVa} span R3?

A: Given vectors, v1 = 06-2 , v2 = 0-38 and v3 = 4-1-5 These vectors will span ℝ3 if they are linearly…

Q: Solve (y(1+1) + coxy) dan + [n+lope-nsmy] =

A: 25. The given differential equation is                                     y1+1x+cos ydx+x+log x-x…

Q: Use Cramer's rule to solve for z. Зх — 4у + z %3D 3 2х + 3у = 8 5y + 8z = 11

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Q: Let C: |z-i=3 and I = §. dz 2z dz. Then %3D

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

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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: Find the angle between x and x4 in C[0,1] with its standard inner product.

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Q: Let 1 an(r) : u(reie)e ino de %3D Prove that:

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Q: Prove that fdr %3D dSxVf

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Q: Which condition would prove AJKL - AXYZ? K Y 56 7. JL XZ 造=8 KL 8 JK %3D XY

A: We have to find which condition would prove ∆JKL~∆XYZ.