It Question : Ins -(第) IRS in Let Xに Xz= Find leng ths f xi, Xz and inner product of Xı, Xz の Frnd coso for the angle and Ke be tween and inner product ( Xe, jnG> f xe, X1 Find unit vec tor Fad vectv projeetion P of Xe onta x, d-8 Tメ p pom

Q: v dA , R is bounded by r= 2– cose R

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Q: i) True or False: T = {0, R} U {(-o, a]: a € R} is a topology on R.

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Q: Let C:/z|=1 in the counterclockwise direction and I = $. Lnzdz, J = §. dz, and z+5i K = $. tanzdz.…

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Q: Evaluate F dr where F(r, y, z) = (2.75yz cos(ryz), 2.75rz cos(ryz), 2.75xy cos(ryz)) and C is %3D 1…

A: Here we will find out the required value.

Q: ?) Evaluate CC xdv where E the bounded where E is Hhe bounded 2 by the para bo loid *=4yt 42 and yhe…

A: We have to evaluate the value of ∫∬Exdv,where E is bounded by the paraboloid x=4y2+4z2 and plane…

Q: if a = 2, b = 6, c= 3 2. Let f(2) = x2 + iy? where x and y are the real and imaginary parts…

A: For the solution of the problem follow the next steps.

Q: Let C:2-1 in the counterclockwise direction and I= 4. Lnzdz. J= 4. ždz, and K %3D $ tanzdz. For…

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Q: Let C:z-1 in the counterclockwise direction and /= Lnzdz, J $. zdz, and K = %3D . cotzdz. For which…

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Q: Tnd he aa t the shaded egen eneloset by the talloutng tinlons 12 Set up the rleg that ge th REA f te…

A: Draw the graph and find the integral:

Q: verif y that the funstio n $(x) VI-x² defined overthe loter val E sati'sfies the coad itions of…

A: Verify rolles theorem

Q: (c) Let D be a region for which Green's theorem holds. Assume that f is harmonic on D. Prove that se…

A: We have function f which is harmonic on D. That is: ∂2f∂x2=-∂2f∂y2 We need to prove:…

Q: Let C: |z+1|=4 and I = 9c 72-1 4z2+4 dz. Then I=0 by Cauchy-Goursat Theorem None of these 1=4nti I=0…

A: using cauchy residue theorem...

Q: (oet ber the following model Y: X, B + X. B, + € Where aue mathices vec tors and B; aNe vectos K; x…

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Q: Evaluate y xz dV, where Wis the domain bounded by the elliptic cylinder = 1 and the sphere x? + y +…

A: We need to evaluate ∭Wxz dV, where W is the domain bounded by the elliptic cylinder x29+y216=1 and…

Q: Let C:z-1 in the counterclockwise direction and I=6 Lnzdz. J .dz, and %3D %3D 2+5i K tanzdz. For…

A: Cauchy goursat theorem is applicable to analytic/holomorphic functions. If a function F is analytic…

Q: Let C:z|=1 in the counterclockwise direction and I = ¢. Lnzdz, J = $. zdz, and K = $. tanzdz. For…

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Q: where C is the circle |z = 3i| =4. 2.3 Use the Cauchy integral formulae to evaluate 22 1 (9 – 22)(2…

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Q: K is the midpoint of GI and HJ. Complete the proof that AGJK = AIHK. Statement Reason Given 2 Kis…

A: A. K is midpoint of GI. B. HK=KJ

Q: dz, J = $. Lnzdz, and Let C:z|-1 in the counterclockwise direction and I = §. K = $, tanzdz. For…

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Q: 2. Given: AB = AD; AACB and AACD are right triangles. Prove: AACB = AACD A B. D. 3. Given: KM 1 JL…

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Q: Prove : Yo=OZ Y z. Statements Reasons XY=XZ, XOLYZ Given XO is the 1 bi sec tor of Y Z YO=OZ %3D

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Q: If the region R is bounded between two circles 961 x² + y? = 4, x² + y? then we have: 2л 3 sin(Vx2 +…

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Q: Let 0 be the angle between the line y = mx +band the x-axis. Prove thatm = tan 0.

A: The question should be :                 Let θ be the angle between the line y=mx+ b and the x-axis…

Q: 6. Write a two column proof. U Given: OSTUV Prove: AVXS = ATXU OSTUV Given T. S Opposite sides are…

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Q: Let C:z-1 in the counterclockwise direction and I= $dz, J = . Lnzdz, and z+5L K = 6 tanzdz. For…

A: Cauchy Gourast theorem: Suppose that function 'f' is analytic in simply connected domain D, then…

Q: 1. Prove the HL Theorem. Hint: Construct RY that is congruent to AL. Prove that AROYALEA by LL…

A: The first question is incomplete. It did not introduce O, E, A, J. So I will solve the second…

Q: 2.1 Evaluate la Im(z – i)dz where C is the contour from z = 1+ 2i to z = i and from z = i to z = -i.…

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Q: 12. Evaluate by using Stoke's Theorem [sin z de - cos x dy + sin y dz] where C is the boundary of…

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Q: theorem to evaluate f.di, where C. (6) Veri fy that レt the circde x² ty? 16 to kes' 2 2=5. holds a…

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Q: 5. Let X = R? and define d, : R? ×R² →R by d (x,,y,),(x,,y2)) = max {x, – x,|-\y, -y}} . 13 a)…

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Q: 23 +3 Evaluate the integral dz, where C is the circle (a) |z + 3| = 3, (b) |z| = 3, (c) |z| = 7. 22…

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Q: the proor that MZXWY + MZRTU = 180°. V R T. U Statement Reason Given VX || FH Given SU | FH 3 ZXWY E…

A: Given problem:-

Q: Consider the figure below. M N PM = PN,LM 1 MN,MN 1 ON LN bisects ZMN0,0M bisects ZLMN Given: Which…

A: Option  (b)  is  correct

Q: Let C:iz-1 in the counterclockwisc direction and I=6, Lnzdz,J-6, dz, and %D 32 245i K tanzdz. For…

A: For K only

Q: Let C:z-1 in the counterclockwise direction and/- dz, J = $ Lnzdz, and K-4, tanždz For which…

A: We are asked to find where the Cauchy Goursat theorem applicable. So, first we state the Cauchy…

Q: Let C:z|=1 in the counterclockwise direction and I = $. Lnzdz, J = §. zdz, and K = %3D $, tanzdz.…

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Q: Utt uxx; 00 u(0, t) = u(1, t) = 0; u(x, 0) = 0;u,(x,0) = 1 u(x.t) = 2(1-cosna) sin(nax) sin(nat) a.…

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Q: Let C:z|=1 in the counterclockwise direction and I = 4, Lnzdz, J = f, zdz, and K = %3D %3D $.…

A: Cauchy Goursat Theorem: A function 'f' is analytic on simple connected domain D containing a closed…

Q: i) True or False: T = {0, R}U {(-x, a] : a € R} is a topology on R.

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Q: 23 +3 22 + 3z – 10 4. Evaluate the integral dz, where C is the circle (a) |z + 3| = 3, (b) |2| = 3,…

A: Disclaimer: Here I have solved Question number 4 and Question number 5 It is given that…

Q: 11. Let F(r, y) = (ry', yr') and let C be the boundary of unit square: 0 Ss 1, 0< yS1. Use Green's…

A: That's easy. Have a great day!!!

Q: M Given: 2TME LPRE E TP bisects MR Prove: ZEPR LETM R Statement Reason 1. ZTME = LPRE 1. • Given 2.…

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Q: Evaluate w xz dV, where W is the domain bounded by the elliptic cylinder + = 1 and the sphere x? + y…

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Q: Let C:z=1 in the counterclockwise direction and I = . dz, ] = f. Lnzdz, and z+5 K = $, tanzdz. For…

A: Here we will check whether the function is analytic on given region, And then will decide the…

Q: Let C:z|=1 in the counterclockwise direction and I = . dz, J = f. Lnzdz, and K = $. tanzdz. For…

A: For K only.

Q: B) Use Green's Theorem to evaluate /F-dr, where C is a triangle from (0,0) to (1,0) to (0,3) to…

A: We will use Greens theorem here

Q: 2.1 Evaluate la Im(z – i)dz where C is the contour from z = 1+ 2i to z = i and from z = i to z = -i.…

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Q: (e) Pruve that the funetion d : R" x R" R* detined by d(x, w) = V(- )+ (- )+ +(, - %3! isa metrie on…

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Q: Let C:zl-1 in the counterelockwise direction and I = 4, Lnzdz, J = , ždz, and K - $, tanzdz. For…

A: Last optiom is correct  That for only k we can apply cauchy goursat theorem