1.) (2a* –be)(ša² +3bc) (x*y-5z')(x*y–42*) 2.)

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

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Q: Find 3²y of z = In(xy)

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Q: Use AAS to prove th Given: ZR and ZP a QR || SP

A: Given that, ∠R and ∠P are right angles. QR¯∥SP¯ We have to prove that, △QPS≅△SRQ

Q: 2 1-X ie 2=tny then prove that da

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Q: 2. Find all volves of tand u x(t,4)=0 and simultomebusly such that =0. 3. 5x-11* C.

A: Get the equations for:  fx=0fy=0 15x2-11y=0-11x+3y2=0 or 15x2=11y3y2=11x

Q: () = 2 sec(a O conon1 O pton 2

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Q: 5. Prove OR disprove that Z/2ZOZ/3Z is isomorphic to Z/6Z

A: To prove or disprove that  Recall that , Now to prove or disprove that  These elements of these…

Q: ) show that 2n" + 1 1+ 222 2n t hence %3D n (n² + 1) 2n4 +1 by first expressing evaluate integrand…

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Q: 6. Find a²z дгу of z = In(xy)

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Q: 1 dæ using the residue theorem. (2² + 1)° Evaluate the improper intergal -00

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Q: Q1. Verify Euler's theorem for the homogeneous funetion, fxy.2)-axy +byz + czu

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Q: 12. Find the general solution using Reduction of Order: а) у" 3DIn x

A: Since you have asked multiple questions in a single request we would be answering only the first…

Q: Find the infimum and supremum of the set X = {3 – Vztn ine N}. -

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Q: Compute 4n — бп? lim Vlan| for a,n %3D 3n2 +7 n-00

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Q: Find дхду of z = In(x² – y) %3D

A: Derivatives can be defined as rate of change of function with respect to an independent variable. It…

Q: Find the rank of A= = xS+ x + invertible. [exham S] O A MOITERUD 225 10-4 and explain why it indic 4…

A: NOTE: Refresh your page if you can't see any equations. .

Q: Prove of disprove if the given DE is exact. 2x^2 +4 =2(3-x^2y)y'

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Q: i) Find an upper bound for the modulus 3z³ + 5z + 1, if |z|<1 where z is the complex number.

A: Now for the mod function: : a+b≤a+b. SO using the same method in the given complex function:…

Q: Prove inf { ñt nEN}= %3D

A: note : as per our guidelines we are supposed to answer only one question. Kindly repost other…

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: 7. Find a pair of integers (x,y) such that 4021x + 2014y= 1.

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Q: Prove that Lim + Tene + …+: 1 %3D ... 2n²+1 V2n²+2 2n²+n.

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Q: Use Euler's method to obtain a four-decimal approximation of the indicated value. Carry out the…

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Q: 1 6 [: 2. Let %3D matnix c (by tnial and erron) Constauct a C (by tnial and eror using anly !,-1 and…

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Q: Exercise.2 Prove that cos-1 z =- In(z ± Vz? – 1)

A: The given problem is to prove the given inverse complex trigonometric identity. cos-1(z)=1/j…

Q: 2 1 Find a mat rix P such that P- 2 0 0 3 0 3 [11 O AP = 1 0 -1 0] BP = 1 1 1 1 OCP = 0 1 1 -1 ODP =…

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Q: 0, 2 is defined by A natural cubic spline S on 5. So()12x - 0 if 1 (1) S(r)2b(x1)c(x - 1)2d(x - 1)…

A: 5.Note that, the natural cubic spline must satisfy the conditions

Q: Verify Eular,s theorem for z =ax2+2hxy+by2

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Q: such that ab = 1 b) : In Z3XU3, Find the order of (1, 2). Show your work.

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Q: (b) State Heine-Borel Theorem.

A: (Heine-Borel Theorem). A subset A of R is compact if and only if A is bounded and closed (with…

Q: Using the 2-transform solve Untz + 4unti 734n=3" with u-0,, =1 %3D

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Q: two positive iontages and bare by 2, them prove that. (2° +1) is most divisible by (2²-1) let a with

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Q: prove that esch'x - In (* + x2 %3D

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Q: IRI- 2. <| sinz|< -e 2

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Q: 6. What is the coefficient of x'y" in the expansion (4x + 5y) s. Show your work here:

A: We find coefficient of x7y8 in the expansion (4x+5y)15

Q: 16) 1. ZDX 2. -X Show Your Work Valid Invalid

A: We have: Z⊃X~X ∴~Z    This can be written as Z⊃X∧~X⊃~Z  Here, p⊃q means "if p then q" This argument…

Q: 9. (a) Express 2 2¹-1² as partial fractions. (b) Hence, compute the exact value of the following…

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Q: Assume that (8) ∞∑n=1nanxn−1=∞∑n=0anxn∑n=1∞nanxn−1=∑n=0∞anxn for all x, and determine what this…

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Q: 24. Find the Fowrier r fas - -IN X

A: Hv

Q: 5) Prove that d tanh ) |-x2

A: Prove that  d/dx[tanh-1x] =1/(1-x2)

Q: Verify Eular's Theorem for z=ax²+2hxy+by2

A: According to Euler theorem,  x∂z∂x+y∂z∂y=nz Where n is the degree of the homogeneous equation.

Q: 1. bility and find the cofact +22=1 %3D - = Z to waishs buing

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Q: Find Š Clim sup and s Clim inf) nt (-1) (znt) of Sn=

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Q: Q-5 Consider NLP problem, max 8() --2+ 2ィ-ズメューメュ+1 ダ」ン0 ズェン」 19 (2). Satsty fnst1 2nd order. For ist…

A: Given: Let's consider the NLP problem max sx=-x12+2x1-x1x2-x2+1 subject to x1≥0x2≥1,xa=12,1  satisfy…

Q: 5. Use Cauchy's Residue theorem to evaluate dz; Có lz-il =1 (2+1)

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Q: consider fixi) = %3D show that trany2 eloes net suhsty kipschifzconchition elo muiswechenclndes ino…

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Q: Prove that le-2z| 0.

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Q: Show a complete soluton 2 3 CO-10y 10sin x

A: Given:

Q: 4. Find the number of surjections from {1, 2, ..., m} to {1, 2, .. ., n} such that no element in the…

A: We have to find the number of Surjection from one set to another set.

Q: if :z = cos 0+isin 0 2z² z²+1 prove that: 1+itan 0

A: