1. w = sena cos ß 2. W = w u+v 3. f(r,s) = rln(r² + s²)

Q: 4. Evaluate fe fds where f(r, y, z) , ) and 0 <t< 1. = 12r2 and the path C is given by r(t)

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Q: Choose T or F* y"+2y' +5y = cos(3x)-sin(3x) ( True Fouls Yh=c1 cos (2x)+c2sin(2x) yp=A cos (3x)+ B…

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Q: 1- Find the solution to the vibrating- string problem With Uu = c*uxx , u(0, t) = u(l, t) = 0 3nx…

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Q: A B с E LL [Choose ] [Choose ] f(x) = 5cos(x) f(x) = cos(x) -4 (x, y+5) f(x)=cos(x)+ 5 (x, 5y) (x,…

A: In this question, the concept of transformation is applied. Transformation A transformation is a…

Q: Find the value of ds / du at u = 2 if s = t2 + 5t andt = (u2 + 2u)1/3.

A: We first find ds/dt and dt/du

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 general solution of the DE y"+ y = x is def ined by (y= C¸ cos(x ) + C¸ sin (x) +x 2 (y=C¸ cos…

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Q: 6. Prove that for x > -1 then Vn E N, (1 + x)" >1+ nx .

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Q: Suppose w = 6xy + In(4 + z²) , x = - , Y 3u + 9v, z = cos(8u). Find dw/dv when u = -5, v = -6. dv…

A: *to find:- Partial derivative of w with respect to v, when u = -5 &amp; v = -6

Q: -2+z) ds over t e point (0, 0, 0)

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Q: -5TT/6 -21/3 -TT/2 -TT/3 -TT/6 TT/6 TT/3 TT/2 21/3 5TT/6 -2 y= 3cos(4x+2T) + 1 Ob. Oc. y= - 2sin3x-…

A: Check by points

Q: -If u = x2 tan-1 २|४ y = - y² tan-1 x 22u дхду x² что - у² + J²u u ә2u u дхду дудх L ala 2

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Q: 2xy + In(8 + z²), x 7v2 ', y = 9u + 3v, z = cos(4u). Find dwlðv when u = 5, v = 2. Suppose w = ,X =…

A: We have, w=2xy+ln(8+z2) x=7v2u,y=9u+3v,z=cos(4u). Point (u, v)=(5, 2)   As we can see that x, y and…

Q: solve: 3 (b) uloy) = ity ² "x = 0 w(x, 3x) = sin x = 0 Wyy u(x,0) = sin x wy (x,01 = cox { (c) in R²…

A: Solution

Q: 1 prove that | e -ym dy = mr(m) -ут

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Q: ー28- Sa Oclumina f dz sabishy cauchy- Reimon quakir f andlgove @ frz= J-2xy ti C-Xyz] +z* @ f(2)=…

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Q: S Prove that L(cos 3t) : %3D (s2+9)

A: We know that Lf(t) = ∫0∞e-stf(t) dt Then Lcos 3t = ∫0∞e-st cos 3t dt                             (1)…

Q: Example 8.10. Evaluate Sº (ii) Simpson's 1/3 rule, (iii) Simpson's 3/8 rule, dx Jo. 1 + x² by using…

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Q: 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 –…

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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: 4. Derive the D'Alembert's solutiojn to the following Cauchy problem Uxx, - 0 0 u(x,0) = e, u(x, 0)…

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Q: Are these equation separable 1.s2+ds/dt = (s+1)/st 2.dr= b(cosx dr+ rsinxdx) 3.y'=ye(x+y)/(x2+2)

A: The objective of the problem is to determine whether the given equations are separable. A…

Q: az az and as Use the chain rule to find at (=) Z = tan V u = 8s + 5t, v = 5s – 8t az as az at

A: Topic:- derivatives

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: Fird XCK) is X(2) = 2くz-)(マ-3) Ans; SC) ャu(k)+と)uck)

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Q: 7. Suppose that f (x, y) = e" cos TY and u? – v², y = u? + v?. x = Using the chain rule, compute the…

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Q: + 9y = 9 sin 3x (Let y p = Ax sin 3x + Bx cos 3x.) y = C1 sin 3x + C 2 cos 3x - x sin 3x + cos 3x y…

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Q: A₁ Let 2 + sinh (2²) - ₁₁ = 27 where w = f (x, y, z)- 1 पुर Find aw дх Jw and Iw > zw. ay dz 3/20

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Q: If fufe.- fuave diffa Veubable at'xo eI fuave difle Veubable at Xo eI Pi:I R,ists-n prove O…

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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: If f(z,y, z) = I COs(2y – 2). compute and af and Te Əz =I Cos(2y -2). compute O = cos(2y2) I sin(2y…

A: If fx,y,z =xcos2y-z....icompute dfdx and dfdz

Q: S 1.Prove that L (coswt) = %3D s2+w2

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Q: Solve the problem: u – kuxx = e-t sin x , 0 0; satisfying the conditions u(0,t) = 2n, u(t, t) = 4n,…

A: Let the transformation ux,t=vx,t+Ax+B ...............(1)uxx=vxxut=vtthe problem ut-Kuxx=e-t sinx…

Q: 1 SS() di = 2t dt volt do T. |3D -/½ 1 tsin(nt), cos(nTt) (na) 21 cos(nt)dt= 2|tcos(ntt)dt= 2 = 0 n…

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Q: Determine the general solution for following Cauchy-Euler Equatio dy + 7x +5y = x³. i) dx2

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Q: 17. (D+ + 2Dz + 1)y = 5– 3x2 a. y = (C, + Czx) cos x + (C3 + C4) sin x – 3x2 + 17 b.y = (C1 + Czx)…

A: As per the company's guidelines we are supposed to solve first question for you, kindly repost other…

Q: 3. Given that 2 = 6²¹ sin (u + ), e2v Use chain rule to find az/0x when x = 0, y = 0. u=e¹ - sin (y…

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Q: 1 Evaluate | (x²sin y- xcos(y))dy O 2sin y-3cosy + C 6 -3sin y+2cosy +C 6 x2(1- cos(1)) – xsin(1) +…

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Q: In GL(2, Z,,). det

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Q: 10- If f(u, v, w) is differentiable and u = x - y, v = y - z, and w = z - x, show that fe fe fe = 0.…

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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: 3. If f(x,y,z)= In 4 xyz Ite t3y:²s²) , find f,,f, and f..

A: Given that: f(x,y,z)=lnxyz4+e-(3xy2z2)

Q: If you are trying to solve f et dx and you let u = e then: dv = du = v = vdu Write down the uv –…

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Q: In AXY Z, the mZY = 90°.XY = 19 and XZ = 22. What is cos X? ООО О

A: Given,

Q: Find fCx) if flo)=0 and the tanGat (k,F CX) has ine af Slore x(x+2) a

A: Given for the function F(x), F(0)=0 and tangent line to F(x) at x,F(x) has slope xx2+23.

Q: + 8z7 – 5 sin z)dz O 4e -z +5cos z +e O 4e +z" +5sin z +e O 4e +z* - 5sin z +e O 4e +z – 5 cos z +e…

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Q: 2/ Compute fc E.dr and Where F Gxry2=(3+ 12x²,3xy²2 is a line segment from Co,01 to (4,2) %D Fdr =

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Q: Hw/ Find if Oy=35x In2x ® Y = x?cos3x. lnx x] ® Y = e*lux cosx Ans/e {(+hox)cos x-lnx.sinx} x. e*…

A: We’ll answer the first question since the exact one wasn’t specified. Please submit a new question…

Q: 2. In AXYZ, PQ || XY . If XZ = 15, YZ = 12, and ZQ = 8, what is ZP? 2.

A: Use concept of similarity. In similar triangle, ratio of corresponding side are equal.