Let C be the shortest path that connects z to ri and /= J, (sinhz + 1)dz. Then O 1 cosh r+ n(1+) O None of these O -snh n*R(1) O snh m n-1) Ocoshn 1)

Q: that the équation /zr2/=/2+3i1 line and it distance %3D Flephe dents the guigen rem 26

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Q: H⋅w. and dwy for the following functions du OX ०५ 2 x+3y² e I_ _w=x²³ tan! ( _ x² + y² 2- W x+y √x²…

A: Note: Since we only answer up to 3 sub-parts, we’ll answer the first 3. Please resubmit the question…

Q: 13. Prove that dx ≤ f √√√x x+1 2 1/7/3 (Hint: use Cauchy-Schwarz)

A: Given:∫02xx+1dx≤23

Q: 28) To evaluate S dt we could use the substitution a) t = sin(u) b) t = tan(u) c) t = sec(u) d) t =…

A: Note: Since you have asked multiple questions, we will solve the first question for you. If you want…

Q: Find the values of a and b that makes f continous everywhere if  f(x) =

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Q: aw and ar Q2) Find if as w = 2x + 4y - z, r+s X =r tan (s), y= sin (r - s), z=e**s.

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Q: Let /- a 8 ddydx Our aim is to write an equrvalent triple integral in spherical coordinates…

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Q: - C "sin" ar sin mæda and Jn.m=" sin" x cos mxdx. and Let In,m= (a) Prove that for m, n ≥ 1, (m+n)…

A: In,m=∫0πsinnxsinmxdxJn,m=∫0πsinnxcosmxdx

Q: snip

A: Given, cosjx,coskx, ∋j≠k, k≥1 if inner product of two function f(x), g(x) on the interval [a,b]…

Q: cos ax -dx = re¯ª,a>0. .2

A: With the help of Residue we can prove given result:

Q: 5. Let F= [3,2,1] and r= [2,1,–3]. Compute the following: %3D a) Proj „F. b) Orth rF = F – Proj „F.…

A: We know that  ProjrF=r.F∥r∥2r Now, r.F=23+12-31=5 ∥r∥2=r,r        =2,1,-3,2,1,-3        =22+11-3-3…

Q: 5] What is the particular solution ( yp) of the ODE ( dx +y 4e*)? a) Ae* b) Ax³e-x c) Ax2e* d) Axe-x…

A: Question 1 is soly.It is against the policy of bartalby to solve more than 1 question. Here is…

Q: FOo=X-1 de fined 2n E- lro] show that Fis Riemenn integruhk

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Q: Let z(x, y) = xe* + sin xy + y - In 2 then a a) -In 2-2 b) In 2-2 2 c) 2 (²-1) d) - 2 (²+1)

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Q: どタ -e -at u Ct) = (a +jwjñ+!

A: To prove that tne-atut↔n!a+jwn+1 It is known that  ut=1 , t>0=0, t<0 Therefore,…

Q: 9)Se-e* dx = -e-x ex+e-x a) Inje* - e-*| +c b) In |+c |e*. c) In Inle* + e*+c d) Inle* + e*|+ c

A: According to our guidelines, in case of multiple questions we should answer the first question.

Q: 29. Show that the functions (x) = sin mx, m = 1, 2,... are orthogonal over the interval [-, ].…

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Q: The path integral v. dr, where v = direction) is given by (sin y, r- cos y) and C is the perimeter…

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Q: 1-) L [ 2 sin ½ t cas ½ t) {

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Q: 2) al X,X2 =) y = Xi~ ? ,-,Xn ~lid exporen tíal ( 100 b) Xq, X2,--- Xn~ iid N(44i44)= ビ- ~? i=1 %3D…

A: Solution : a) Given : xi  ~ exp ( 44100 )   ; i = 1,2,3,...,n ∴ θ = 0.44     Y    = ∑1n Xi It is…

Q: show that f in Vienann and findit Limibs 2. 0 FC)= X 2) fCX) = -X? iXE [011] XEE-li0] %3D %3D

A: (1) fx=x2 , x∈-1,0 ∫abfxdx=∆xfx0+fx1+fx2+......+fxn-1 Where ∆x=b-an we have that a=-1,b=0,n=4 ∆x=14…

Q: QUESTION 6 Let fo(x) = nx2 +5 for neN and x ER 4n +3 1. Show that (f.(x)) converges uniformly on [ -…

A: Since you have asked multiple question, we will solve the first question for you. If you want any…

Q: 1) Find ôz l ôu and ôzlôv for z= 4e* In(y), x= In(u cos(v)), y=u sin(v) at the point (u,v)=(2,7/4).…

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Q: O If z-frxy) show that つる

A: As per our guidelines we are supposed to answer only one question. For the solution of the problem…

Q: Evaluate the integral. 28) sin dt A) -cos B) cos C) 5 cos + 6 D) COS 1/5 +

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

Q: Classify the Stries as nbsolurehy linvergen ti Condibinally lonvergent, divergent 18 K Sin

A: First we  recall some definition-1)  p-test for convergence of series ∑k=1∞1(ak±b)p :     A series…

Q: Hw4 Prove if x;-→x then if xj ->x Hw4| Prove and HoS Prove if x; →× y;→y > X

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Q: 3) sinhz = z *, 8WJ ทรู) 2n 3 (en-j

A: We know,        sinh(z) = (ez - e-z)/2 Now,        ez = 1 + z + z2/2! + z3/3! + z4/4! + z5/5! + . .…

Q: 2 Ql Eind dyldxf x+3X+4= Cos y

A: Differentiate w.r.t x

Q: Vee the definition of the downtie! Find filx) then find fil-2), f'(0), and fi(3) 12 - X 3 b.) f(x) =…

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Q: EX Pand Pa= Va lid for ocl2-21<3 9s laurentSeries (2-2)(1+2)

A: Laurent series of a complex function f(z) is a representation of that function as a power series…

Q: How can we prove to get dual from primal standard form? from this primal standard form Max.z = c'x…

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Q: O C = Paith 4: 3+ las t+ I sint t=0.

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Differential Equations

Have you ever observed the movement of the satellites and rockets or how the planets go around the sun in their orbits? How will you determine their motion? Definitely they follow some scientific laws and these kinds of problems are framed as differential equations.