8 15 Va 8 dx Evaluate 3 5 12 x 4 – In(x®)+12 x 3 + C, Where C is the parameter 5 - - 12 x 4 – [In(x)]8 + 12 x 3 + C, Where C is the parameter 5 - 12 x 4 – In(a*) — 12 ӕ 3 +С, Where C is - - the parameter - - 12 x 4 – [In(x)]$ – 12 x 3 + C, Where C is the parameter - -

Q: 1 Let f (x,y) =In Then f (1, – 1) =... 3x2+4y3 XX

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Q: 5. A clamped cubic spline S on [0, 2] is defined by So(x) – 1+ Ar + Bx - 23, 0<x < 1, S(x) – S1(x) –…

A: Using the conditions of cubic spline,

Q: f(In x)2 dx O-r(Inz)² - zlnz+z+C -z(lnx)² + zlnz+ 2z+C O-r(Inz)² - zlnz+z O None of the choices…

A: The objective is to integrate the given function Use integration by parts, which states that…

Q: 5. Use Green's theorem to evaluate where C is shown below (6y - 9x) dy — (xy - x³)dx (-1,4) (-1,-1)…

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Q: 1. Let f(x, y) = In(x - y) then at the point (4,1), fryis equal to: %3D -1/9 O 1/7 1/9

A: Thanks for the question :)And your upvote will be really appreciable ;)

Q: The domain of the funsfon f(x) te 9) E2,21, or equivalenfly,t243 C) [4,00, 0r )(00,4),or…

A: This question can be solved by applying the concept of existence of function at various points on…

Q: (2) = [| (a) %3D h (b) Value(s) that are NOT in the domain of -

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Q: 18.7. Let f(z) = (e + e-2)/2. Evaluate f(2) -dz, where y is any %3D simple closed curve enclosing 0.

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Q: 33. x-t= T2+1 35. uv = x + w2 37. x- abc = a³ 39. a+ bc = x- cb 34. w= 36. 13+x= T³ 38. mn2 m3+ x…

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Q: 15.4.59 Assume that F(x.y,z(x,y))3D 0 implicitly defines z as a for xyz + 8x + - 4z = 0. dz

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Q: 6. Let u (r, t) be the solution of the initial-boundary value problem ut = 9uzz 0 0, %3D uz (0, t)…

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Q: | [5æ1+ 4 et + 6ª – 8] dæ + 6* – 8 dx Evaluate : O In(x)³ + 4e%æ 8х + C, Where - In(6) C is the…

A: We will use standard formulas of integration here

Q: solve Qno7

A: You say to solve the question number 7 .ok y"' +6y"+12y'+8y=12e^-2x

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

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Q: Show that (0, 0) is a critical point of ƒ(x, y) = x2 + kxy + y2 no matter what value the constant k…

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Q: 9. z = xe-; P(1,0, 1) 10. z = In /x² + y²; P(-1,0, 0) 11. z = e³y sin 3x; P(7/6,0, 1) 12. z = x/2 +…

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Q: Find for x = x(t) defined implicitly by 25+25 x In(t) = e25xt Also evaluate dt at (t, x) = (1,1).

A: Given,25 + 25xlnt = e25xtTaking 'log' with base 'e' on both side, we getln25 + 25xlnt = lne25xtln25…

Q: Find solution of an equation X f(x) 1.0000 1 1.25 0.8000 1.50 0.6667 1.75 0.5714 2.0 0.5000 a. Using…

A:

Q: 3. Using integration by parts (IBP), what should you pick for u and du in 5z cos(3r) dr? = cos(3r),…

A: Integration By Parts formula is used for integrating the product of two functions. This method is…

Q: Q3: Use finite difference method to solve Laplace equation in the red (hand written plzzz) domain…

A:

Q: 2. A firm produces two goods in pure ompetition &amp; has the pllowing TR &amp; TC functions R= 15Q…

A: In this question, concept of optimization is applied. Optimization Mathematical optimization is the…

Q: 8.1.33 Evaluate the integral belov 20 + y dy 20 - y - 20 20 +y dy = (Typ %3D 20 - y - 20

A: Solve the integration by substitution method and C is integration constand  and use reduction…

Q: 1 Find the Nahee af the falloding in togreals's Jet X+1 3. 8. +3. -4+3 da -2 2 JX -9. 2. Lett-lx 9.…

A: You don't mention which question i have to solve. And you already solved them. I go through all the…

Q: a) z=-3x y² + sen(x²y) 2x c) z=-In (x y³) e) z = x²ln(2x³y) b) w=2xz-3e²xy d) z=2e²y sen(x) f) z=…

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Q: 3- Let µr1 = 2 in region 1, defined by 2x+3y-4z > 1, while µ2 = 5 in region 2 where %3D 2x+3y-4z <…

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Q: 4.18 Given that g(x) > 0 has the property that 196² show that is a pdf. f(x, y) = g(x) dx = 1, 29…

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Q: 4. Let z = x2 + y³, x = 2st, y = s - t2, s = u", and t = u sin w. Compute for Oz ду and дw ди

A: Let z=x2+y3, x=2st, y=s-t2, s=uw, and t=u sin w.To compute for ∂z∂w and ∂y∂u.

Q: 27. Show that कक्या 1 Vn E Z*. T1\2i+1 2i+2. i=0 (2n + 2)!'

A: Consider the given expression. ∏i=0n12i+1·12i+1=12n+2! Consider the left side of the equation.…

Q: 2.7 Given that the spacial components of motion, x = x(X, (), are: x₁ = X₁ + X₂ (e' - K), X₂X₁…

A: Solution : x1=X1+X2(et-K)      …(1) x2=X2+X1(e-t-K)   …(2) x3=X3    …(3) Solving above equations,…

Q: of fxyl = 3X-y+6 Subjected QI Find to x+y=4 extrume v alues

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Q: 1-6 Usc an appropriate form of the chain rule to find dz/dt. 1. : = 3x'y'; x =r. y = r 2. : = In(2r…

A: Note : There are many subparts in the question. So I will answer the first two subparts…

Q: Evaluate : | [5æ1+ 4 e* + 7* – 8] dx O In(æ) + 4e%ar - 8х + С, Where | In(7) C is the parameter 7 O…

A:

Q: 26.Show that if p is differentiable and p(t) &gt; 0, then the Wronskian W(t) of two solutions of…

A: Given: [p(t) y′]′ + q(t) y = 0 W(t) = c/ p(t)

Q: 2. Evaluate ř(t) dt: 4 4t ř(t) t2 + 5t + 6' î + 2e4t cos t j - k; a = 0 and b = 4 t2 + 1

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Q: Əz 1 Q3.If Z= f(x,y)=4e* ln(y), and x = ln (u cosv), yusin v, use chain rule to find : 201 ди and az

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Q: (1+ x^2 )dy + 2xydx = 0 * O c= yx sin(x)+y O c= y+ In(-x/4) O y1=x^4(C- In(x)) O y = 128 + Ce"(-x/4)…

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Q: 6. Suppose f(2) is analytic in |2| 1, and f(0) = 1, f(0) = 2, compute: %3D (1) h = fe(s+ 1)2d: (2)…

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Q: 21. xª sen z dz -z' cos z + 3z² sen z + 6z cos z 6 sen z + C %3D

A: see below the answer

Q: Q1 : prove 1 2(1–z) 3(1--z) dydxdz = 1

A:

Q: 3) yv1+x²dx + x/1+y?dy = 0 (1+v1+x²)(1+/1+y²) Ans: V1+ x² +/1+ y² In +c (Bali, 2007) xy

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Q: 1. y = Ax² + Bex 2. y = C₁ ex cos3x + C₂ ex sin3x 3. y C₁e* + C₂e²x + x 4. Iny = C₁e* + С₂е¯* 5. x =…

A: As you have asked multiple questions so that I have answered first question as per the guidelines.

Q: 2. Derive a formula to approximate S* s* f(x;y)dxdy yo xo Using Simpson's rule with x2 – xo = 2h ,…

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Q: 3. Find the general solution of xy' = x – y + xytanx a. xycos x = xsin x + cos x +C b. ycos x = xsin…

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Q: 1. x = sin(t)(3 – 2 sin(t)); y = cos(t)(3 – 2 sin(t)) sin(t?)) 2. x = cos(t²); y= e 1 1 1+t2 1+t² 3.…

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Q: 15.If the Wronskian of f and g is t cos t − sin t, and if u = f + 3g, v = f − g, find the Wronskian…

A: Consider the provided information, Wf,g=fg'-gf'⇒tcost-sint ...... (1) Find the Wronskian of u and v.…

Q: 1 Let f (x,y)=In . Then f „(1, – 1) =...... 3x²+4y3 XX

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

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

Q: 16. If f(x) = 5, (;e* G +5) dt -x, then the inflection point(s) of y = f(x) is(ar- %3D 3 A) x = 4…

A: f(x)=∫0x14t4+5dt-13x4

Q: 1 12 Let X be a single observation from a population with pr 4.12 f(x) = 1+6² 0<x where 0 is a…

A: From the given information, fx=1+θ2, 0&lt;x&lt;11+θ2 Given hypotheses: H0:θ=0 H1:θ=1 Critical region…

Q: [6 Let f(x) = |r| be approximated by sN(x) = }a0+E (an COS (") + b, sin (7). %3D n=1 Determine the…

A: