.3 If U = 2– x, x/2 - xdx= (A) (2 – u)/ūdu В u/ūdu ,1 © Lwūdu uvūdu .3 D J (2- uWūdu

Q: 10. If z = x + f(u), where u = xy, show that dz = x. х дх

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Q: 3-If u(x),v(x) and w(x) Find d/dx of (uvw)

A:

Q: 4. If u = xy + y²z³, where x = rset, y = rs²e when r = 2, s = 1,t = 0.

A: We have to find solution

Q: 5 If u =x² +y² and v = 4xy, determine дх дх ду ду du' dv' du' dv

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Q: E. Prove the following: 四- Iz.l 1.

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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: 2 al S ex+y dydx

A:

Q: € 4. If y=u² and u = x³ + 4 determine dx

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Q: Solve the following first-order linear DE's. y' + (cotx)y = xcscx, y = 1

A: we have to find the general solution

Q: 7) if p(X) =- ) , and grea) =0; g'LW)=), Find f'la). %3D

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Q: 4. 5 Show that if y%= x+4 then dx (x+4)** %3D %3D 16. dx. 2 (x+4)² **n Hence, find the value of|

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Q: .'( , "ג oa3 (125x*y)" 学 A: 125 2 3 $%% 1/3 5メ Y C: D: VONE OF THESE

A: Since you have asked multiple questions in a single request, we would be answering only the first…

Q: 2. Evaluate f. (y²dx + x?dy) where C is the triangle with vertices (1, 0), (1, 1), (0, 0).

A:

Q: 1-y² L In (r* + y? +

A: Introduction: The process of determining the area of the region under the curve is known as…

Q: Evaluate dz where ci) .C is 1z+ Yzl =2 Ci) c is 1ztil=1

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Q: If A = 2x î + 3yĵ – z k and x = t² , y = t and z = t + 2; then the value of ſc À · d¯ from t = 0 to…

A: A = ( 2x, 3y, -z ) and C : ( x, y, z ) = ( t2, t , t + 2 ) for t = 0 to t = 1. We have to evaluate…

Q: The tanh (2x) sech (2x) dx is equal to sech (2x) sech (2x) +C OA 3 10 OB. sech (2x) sech (2x) +C. 3…

A: Solution

Q: 2) Show that (1 – x²)P",(x)P'm(x) dx: 21(l + 1) Sim• 21 + 1

A: Given:-  ∫-11(1-x2) p'l(x)p'm(x)dx=2l(l+1)2l+1δlm

Q: If x= 2u3 – 3u² and y=u³ – 3u, then dy is dx u+1 (A 2u u+1 B и — 1 2u и — 1 D

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Q: Consider the figure below. uestion 1 T. 2x W Зх - 5 Previous

A: Given TW= 2x, 3x-5

Q: 3. If f(x, y, z)= In xyz te(3.0²), find f,,f, and f-· 4

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Q: FIMD dY IF x= AMD Y= U 1tu3

A: Let's find.

Q: For ſ k*e3* dx = 1 (ke)3x 3 (1–In 2-1) + C. If u = 3x, then k =?

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

A: w=5x2+2y2,   x=-3s+t,  y=s-4t

Q: kx 4+x² If k > 1, evaluate O ka -In|x² + 4 +C 2 Okx -arctan (2x) + C 2 Ok In(x² + 4) + C O arctan…

A: Given: I=∫kx4+x2dx   ...1   As we know the common integral. ∫1ax+bdx=1alnax+b+C

Q: S dy 7 y2-8y+5

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Q: 2. and XR %3D C. Two tails with n = 34 , x =

A: Solution: From the given information, level of significance is 0.01 and n=34.

Q: e. y= (x² + 4)/x in the interval 1<x<4. 8+ 4ln4 - % s.u ans.

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Q: 3. If z = f (x, y), where x = e“ – e® and y = e® – e", show that UTM UTM az az UTM X : az - ду dx…

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Q: Evaluate: S ndy 2y+3 (y 1)(y 1) In G) ny² + y + 1| - arct arctan 0 Inly 1| ž(y 1)* nVi y arctan( ) c…

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Q: You hare shown that e jul dw or , erchenying w and t Jlw) = Use a chume of veriables to genenle…

A: Consider the given information: δ(t)=12π∫-ωωejωtdω                  ..(1) δ(ω)=12π∫-ωωejωtdt…

Q: 5) Find NV ir ZN -- 20 7) Find DW if YW-4

A: Consider that the centroid divides the median in the ratio 2:1 (5) ZNNV=2120NV=21NV=202NV=10

Q: 1. Find fr fy and fry if f(x,y) = y* + x?y + In xy.

A:

Q: a?u du k 00 at Subject to the condition u(0, t) = 0, u(L, t) = 0 50x u(x,0) = f(x) = 50 – L. 0<x<L

A: Please check step 2 and 3 for solution

Q: Please see the attached problem. Thanks!

A: Given:

Q: - Given y= ela's -x²-In'r, what is y'?

A:

Q: In(y) 6° Evaluate dy.

A: Consider  I=∫19ln(y)ydy

Q: 3. Obtain the 6.S. sy dx + taydy = 0 xcos

A: We have given equation  xcos2y dx+tany dy=0 xcos2y dx=-tany dy x dx=-tanycos2y dy x dx=-sec2y tany…

Q: If E?uz = x² and h = 1, then find ux. %3D

A: The objective is to find ux. Given information is: E2ux=x2, and h=1.

Q: 6. Evaluate 1 x² + y² + x² dV, where E = { (®,g, z) |1< n? +g? +z? <4}.

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Q: (b) ƒ(x, y) = Vy – x · In (y+x) -

A: Given (b) f(x,y)=y-x ln (y+x)

Q: BeR NOULLI 's EQUOTION (2yーX)d水+ラ×ydy:o ソ+PCx)yq(x) yh XrlwDepenとn 3 y= Depen Dest

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Q: 9. Find y if (a) y = 2" In (cot² (v7))

A: We are authorized to solve only one independent question, please repost remaining questions…

Q: (2? + y? + 1) dæ – (æy+ y)dy= 0 - %3D x +1 (x + 1)? Option 1 Option 2 (x + 1)-3 (x + 1)-1 O Option 3…

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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: In csch 4y d 3) tanh 4y

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Q: %3D in Fin d E(S an d Var(s)

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Q: Evaluate xy dS. S: z = 3 – x – y, first octant

A: Given query is to find the double integral in first octane.