15. x³dA, R=[-4,4] × [0, 5]

Q: 0 2 4 6 2 3 4 5 If A = Compute C1(A). 2589 3 2 1 7

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Q: 7. Remwrite the..either.five.exated.nt.agrmls. 1-X FCX ng , Z)dydzdx ZA z= 1-x2 ...... y=1-メ

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Q: 2 Evaluate: :S,vte-t² dt.

A: Detailed explanation mentioned below

Q: 4. Find the critical numbercs) for gx) =IRCX+1) t, en cuaracterize ealh, one as 1ocal min, or…

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Q: 6. Evaluate In (x - In (r-...))dr in terms of some new variable t (do not simplify).

A: Given :- ∫lnx-lnx-...dx To find the given integral in terms of some new variables t

Q: 1 Show that 2-* d.x 2 In 2

A: We can show the answer in the following steps.

Q: In x /1+ (In x)² -dp-

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Q: Suppose i = (-3, –3, –5) and v = (-1, –5, –1). Then ů x ở is and i x ũ is

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Q: 27. Verify ldt ip|1| =x|x]. Hint: Consider x > 0 and x <0 separately.

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Q: 6.13 Show that t: = B,/[s//E=, (x;- %3D VI- r in (6.20). |

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Q: 2. Evaluate the following dr 2.1.V1-(In)* dr 2.2. VE(1+ z) dr e-e- 2.3.

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

Q: 1 Evaluate [ (x² + --- e2x +c 2 a) + In x+ b) 3 +C 3 e2x .3 c) + In x- d) + In x - 3 +c +c 2 2

A: We know  (1) integration of Xn dx =  Xn+1 / (n+1)  + C  (2) integration of emx dx = emx / m + C  (3)…

Q: х-у If z=x²sinh then дхду 4-

A: Find partial derivatives.

Q: .1כ If n33, еxpand u %3D а'хх, a" x,x;

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Q: 2. alak S 6sin"xcox dx

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Q: 5.43. -- ("*)(*") = ()- in (m+n+: sk=-m r+s+1

A: We have to prove given relation by using counting argument.

Q: 81/ show that *if ve(Xジーズ) oif v=(

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Q: 5.1. Show that y2 , V2 , and v3 + V2 algebraic. are

A: We will use definition of algebraic numbers

Q: Queston #o 4 Show that X, Ixe, where x, and Xe E IR X= (1,1,1, -1) Xz = (4,2,2, -1) %3D

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Q: -2x -dx - Evaluate (1-x)' 8 А. х* + 6х- In(1-х)' + 1-х 8 -(1-x)* +C С. х? +6х+ In(1-х)' +- -(1–x)*…

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Q: dz ニ Z – 2j K K : z |= 1

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Q: -27 -36 81 onstruct it in R. 37, 65, 0,

A: * Hi! Thank you for the question, As per the honor code, we are allowed to answer three sub-parts at…

Q: in(Zg++s)indeyclic grauf2enerated by I, Z,3

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Q: Suppose we observe X1, X2, ..., X U (0, 1). Show that nX(1) 4 Exp(1). с.

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Q: 3. Evaluate Se(x² – iy²)dz along the straight lines from (1, 1) to (1, 8) and then from (1,8) to (2,…

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Q: S Sech (ax-

A: Evaluating the integral of hyperbolic function using substitution.

Q: (19) ds dt t= -1 if 5=1-3t

A: The given function is s=1-3t2

Q: 2л 2 2 Compute |pA dz dr de 0 07 O A. 35 28 O B. 35

A: To solve the integration.

Q: (8) If w = 5x² + 2y², x= -3s+t, and y = s – 4t. Find and Əw as

A: The objective is to find the partial derivatives .

Q: Consider the following LP Min z = 3x, + 2x, +7x, s.t - x, + x, = 10 -2x, + x, – x, <-10 1 Solve the…

A: Given, Min Z=3x1+2x2+7x3s.t,                    -x1+x2           =10              -2x1+x2-x3≤-10 The…

Q: 3. f(г, у) 3D In(х +y)

A: The differentiation of  ln x = 1x

Q: 3sin4t dt 2. 5(1- 3cos21)

A: We have to find integral

Q: If In a + In(z-7) = In(4x), then z = 11 %3D

A: Since you have posted more than one question we solved the first one for you. For the remaining…

Q: 15. Find the general solution of dr bcosedr + rsinode

A: General solution of differential equation

Q: az If x2 + xy + yz + z2 = 6, then- ду

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Q: In(2 + x – 2y2 – 3z), 7 =, then If f(x, y, z) Duf (2,-1, 1) = - A) 11

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Q: 5. Show that xZx + yZry = yezy if z= xy + y In xy

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Q: Suppose X~N(113,18), and Z~N(0,1). Then x = 94, is equivalent to z = ______.

A: Given that, Suppose X~N(113,18), and Z~N(0,1). Here, mean μ=113 and standard deviation σ=18

Q: -bability den= 10 > 7) is:

A: The probability density function is given as, fx=110 for 0≤x≤10. To determine the value of the…

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: Find y' in y = (x³ 3x²(x²+e) x³ +3 A. y' = B. y' = C. y' = +3)(x²+e) +7x6 In (2³ + 3) +7x6 (x³ + 3)…

A: Understanding of derivative when function is there in power of any function.

Q: 8 Show that 1+2++ In S 1|+ |r2|++|rn| for any numbers r1, 22, ....

A: To show,    x1+x2+.....+xn≤x1+x2+.....xn   for any numbers  x1, x2,....., xn . Which is generalized…

Q: 26. If z = In(x² +y²), find x- ду Əx A) х с) у в) х-у D) 0

A: If z=ln(x2+y2), We need to find x∂z∂y-y∂z∂x.

Q: 2. 1. If UZ = x+ 21 and ZS = 3x – 15, find US.

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Q: 2 4-x2 x2 +4 1 2x

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Q: 13. If w(x,y) = In(1+xy²), show that 2wxx + y³Wyx = 0. %3|

A: Given: w(x, y)=ln(1+xy2)  To show: 2wxx+y3wyx=0 Chain rule : ddx(f(g(x))=f'(g(x))g'(x) Quotient…

Q: 10- Prove that a.b3D la+bl2- la-bl? /4

A: Prove that a.b= la+bl²- la-bl²/4

Q: of dr? e-ex

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Q: 16) * Find y' if y In (x2-8), when x 4

A: