if x, y>o such that x Sy then Vã svy Prove by direct method

Q: If z = e'x + y In(x), find z, and z, Zx Zy II

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Q: OLet @ = (0,1)n Q = {x€ @104 x<1}. Prove that %3D 2) 2000m

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Q: (a) Suppose X U (0,n), where n is a positive integer X-[X] U (0, 1). (b) Use the result of (a) to…

A: De Moivre's theorem gives an axiom for computing the powers of complex numbers. We first gain some…

Q: Let f(x, y) = xcosy- y e*y. fry at (1,0)is equal to: -5 3 -1

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Q: gralof 1/x from ac to bc (0<a<b) is the same as th

A: The purpose is to prove that , ∫ab1x dx=∫acbc1x dx The  integral of 1/x from a to b.…

Q: H) 9f zyzec then prove thal nl x=4=Z, (alogen) %3D

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Q: dy is If y = In then cosh z

A: Given,          y=lnxcoshx

Q: Prove that the following ODE IVP is well-posed: where f(t, y) = 1 + t sin(ty). y' = f(t,y), 0< t <…

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Q: az əz 1. ax' dy If z = In(e* + e"), show that %3D %3D

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

Q: Calculus

A: see 2nd and 3rd step.

Q: Evaluate |- e*dz where c is |z|=3 using Cauchy's integral formula „(1+2),

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Q: Prove that fdr = [[ dS×Vf %3D

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Q: 21. Prove that lsio rol ylanoti (i) Res (tan z, x/2) – – 1 1-cos z (ii) Res 12

A: The solution is given as

Q: Q4 If f(x, y) = In(x² + y² ) %3D Prove that dy2

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Q: Let f(t,y) = y+ 3t?e'. Then f satisfies a Lipschitz condition in y with L = 2, given that 1sts2.…

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

Q: Suppose that f(x) > 0 on [0, a], ƒ(x)< 0 on [a, b], ſo“ f(x)dx = 7, and S" f(x)dx = –3. Evaluate the…

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Q: 4. If x = cose + isin0 & 1 + V1– a² = na then prove that 1+ acose =(1+ nx)(1+) %3D 2n

A: Given, x= cos θ+i sinθ and na=1+1-a2      To prove:  1+a cosθ=a2n(1+nx)(1+nx)       Let  x=…

Q: 0/ the Valke of & that makes the Velteof the fumetion 2.

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Q: Let Use Euler's Method with h=.5 ond (X,Y.) -(1,1) to estimate (a, y )

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Q: FIAD THE OTER FIXF FUH aiON OF ĦF xauTF XHGUE X O SIn X =3

A: The given function is:sinX=35To find other five function

Q: Let f(x, y, z) = ln(x² + z) + y²e"z – cos(2yz). Find fzya- CoS %3D

A: use partial differentiation for finding the derivative.

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

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Q: Let R = [0, 1] × [0, 1] . Estimate ſfr 6(x + y) dA by computing two different Riemann sums, %3D

A: Given, R=0,1×0,1 and ∫∫R6x+ydA let us assume that fx,y=6x,y. Here, we required to calculate Riemann…

Q: 2h 1+h )-2 = 1 – if h<<r Prove that ( %3D r

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Q: Prove that E (2s+l)=3n" whenever 'nisa psitre r'nisa pisitive intger. 32.

A: Given that,      ∑j=n2n-12j+1=3n2, n is a positive integer

Q: For the IVP, y'=f(x,y), y=yo, x=xo, iff and df/dy are continuous discontinous defined undefined then…

A: Here we have to choose the correct option.

Q: Let H(x) be an antiderivative of 1sm z if H(5) = 7, then H(2) =

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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: (b) Evaluate the integral fxIn x dx using by parts formula.

A: Answer is:  (x2/2)lnx -x2/4 + C

Q: If f(x, y, z) = In(x7 + yº + z®) + (x° + yº + z®), then find fr, fy and fz at (1, 1, 1).

A: →fx=∂f∂x, During derivative of ∂f∂x, consider 'y' and 'z' as a constant→fy=∂f∂y, During derivative…

Q: dz Find if yz – In z = x + y ax

A: To find the partial derivative of z of yz-ln z=x+y with respect x, differentiate yz-ln z=x+y, while…

Q: Let X,X, X be i.i.d. with the following PMF. ...... 25 0.6 ; k = 1 Pk)= 1 0.4 ; k = -1 and let Y =…

A: Answer: For the given data,

Q: Let BE Cnxn. If z" Bz = 0 for all z E C, then show that B = 0.

A: Given expression is

Q: Suppose that the joint p.m.f. of Y and Y2 is defined by: 2x + y for x = 1, 2,3; y = 1,2,3 54 f(x, y)…

A: The probability mass function of Y1 and Y2 is,

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: Q3/ prove fry = fyx if f(x,y) = x + xy – 5x³ + In(x2 + 1)

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Q: dy is then da In a If y = cosh r

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Q: With integration by parts, J udv · Judv = UV - O True O False

A: Solve the following problem

Q: Evaluate by Cauchy’s integral formula: ∫ c e3z/(z+2)4dz where c: mode z = 4.

A: To find - Evaluate by Cauchy's Integral formula : ∫Ce3zz + 24 dz where C : z = 4     Formula used -…

Q: lx)にX sit. ors<I prove that inl Guernesto uniterady. Guveryes to

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Q: 31. f sen z - sen z dz tag z dz dz cos z -In lcos z + C = In jsec z + C %3D %3D cos z

A: Topic- indefinite integration of trigonometry function

Q: Defn `x→- `xj diverges to minus infinity" VR>O 3N, such that Vj zN *j<-R 8;<- R Hw7 het x; = - 8j…

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Q: Let F(x, y, z) - z* + x+y sin x + x In z- 0, where z- f(x, y), then at (0,0,1) and are az %3D %3D…

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Q: 10. Given: YT = YP, LC = LR, Proof ZT= LP Prove: CT = RP R

A: Consider

Q: If f(x) - g(x) = 1, then f and g have the same antiderivative. %3D O True False

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Q: B. Prove by direct proof general. P: Vn e ZE, (n – 1) (n+ 1) e Z,

A: I have solved B; you just need to expand (n-1)(n+1) and then use the fact that square is always…

Q: 1 (aw C. Ifw=f(x.y) and x=1. coso, y=. sino. Prove that

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Q: If f(x,y,z)=z In(x²ycosz), then fz is O 2z X OZ y O2z y O In(x²ycosz) - ztanz <|N

A: This question is related to partial differentiation, We will solve it using given information.

Q: Expand the function f(x) = tan x up to the first two non-zero terms in the Taylor's polyno- xn+1…

A:

Q: Evaluate the iterated integral 3 1/x 4 = S S yla³ dydæ 1 1/22

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Estimation

A new framework of data analysis where the new statistical methods are used for interpreting the results and analyzing the data is known as estimation in statistics.