If x = u?(u? – 1)² and y = (3u2 – 1)², then what is the value of dy/dx? A) None of the choices (B) В 3(u² – 1) u? - 1 3 D u? – 1

Q: | 21×VX2 + 1 dx = 14 2- 7, what is 21uV u2 + 1 du? Given that %3D

A: The properties of definite integral is ∫abf(x)dx=-∫baf(x)dx. Use the property of definite integral…

Q: If x, y, and z are lengths of the edges of a rectangularbox, then the common length of the box’s…

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Q: 5. If u = e1#1+az#2++anIn, where a² + a³ + · ·..+ a = 1, show %3D + = U dx?

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Q: 2) (1+ e*/y)dx + e*/y (1 – 2) dy = 0 Ans: x + ye*ly = c (Bali, 2007) %3D

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Q: Find af af and f(x, y) = etry In(6y) af 4yln(6y)e^(4xy) af 1/ye^(4xy)+4xIn(6y)e^4xy dy f(x, y) = cos…

A: In the first part the answer is correct but you have mistakenly not taken bracket for 1/y . You can…

Q: e /// 2 Evaluate 2xz dV where E {(x, y, z) |1 ≤ x ≤ 4, r ≤ y ≤ 2r, 0 <z<x+3y}

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Q: • If u = x+ 1 t= yu y = -t² then, %3D 1. dx dy -1 dy = X dx dy 3. dx |3D dy 4. dx 1 O 2 O 3 O 4 O 1,…

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Q: Ex 21Eulers method dy-y= - y Xーツ ーメー

A: We have to use the Euler's Method to solve                           dydx=y'=x-yx+y, y0=1,…

Q: 2 If In(ax)dx = 3, then a = %3D %3D 1 4 4 e4 4 ез 4 O None

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Q: Y = w tan-1(uv), u = r + s, V = s + t, w = t + r when r = -1, s = 2, t = -1 1. as at ar as %3D

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Q: z = x* + xy", x = uv* + w², y= u +ve" dz when u = dv Find 3, v = 1, w = 0

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Q: If x2 + y? + z2 = 9, dt dy = 9, find dt dz when (x, y, z) = (2, 2, 1). = 4, and %3D dt %3D

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Q: - Evaluate the follwoing | r" exp(ax")dx where a + 0 and m+l = 1, 2, 3, ...

A: Given integral is, ∫xmeaxndx Substitute, u=am+1nxm+1dudx=m+1am+1nxm+1dx=1m+1am+1nxm+1du Then,…

Q: dw If w = f(x,y,z) = In(x² +y² z?),x = cost y= sin t ,z = 4VE , then is : dt + ww.

A: Given  w = f(x,y,z) = ln(x2 + y2 + z2) x = cos(t) , y = sin(t) and z = 4t Substituting the values of…

Q: ex+y ди 21. If u = show that ax ди = u ду - ex+ey'

A: The given function is: u=ex+yex+ey

Q: --- Q#3 Evaluate Cf 2x dV →Where E = {(x, y, z)| 0sys 2,0sx sV 4 - ,0 < z y} ,0 sz< y} Ee

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Q: Hiws slove du 4 dt %3D dx2 u(6,t) = L (8,t)=0 U(x, a) =0 : =4X-()x²

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Q: (a) Let I = dx. Show that I² = dx dy. R2

A: Note: "Since you have asked multiple questions, we will solve the first question for you. If you…

Q: dx + AIX y = cos x, y(n) = 0

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Q: 6. Ifw = f(x-y, y-x), then show that, ar + L = 0. dx ay

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Q: Evaluate the integrals

A: 37. ∫112142dtt+4tt38. ∫0edyy1+(ln y)2

Q: (2) Evaluate 6y dV, where E = {(1, y, 1) | 0 < z < ry, 0 < y S 1, 0SISY} %3D

A: The objective of the question is evaluate the integral.

Q: Evaluate /f/2e(*+у*+ dV over B where B - {(a, у, 2) : а? + у? +2? < 1}. Тake п %3 3. SSS 2e(z²+y° О…

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Q: 12. Evaluate (2+ r+3|) dx by interpreting it in terms of areas. Y-3+ 1-4 +3 %3D 2. a dy X dr t 3 dk…

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Q: If f(z, y) = e" sin(4y) then: V f( – 1, 1) =

A: Given function is f(x, y) =e4xsin4y.  We have to find ∇f(1, -1 ). The vector differential operator ∇…

Q: re' dy + +1 dr =0 O (y – 1) e + + In z = C 2. O-(y+1) e + Ine =C 2 O (1- y) e + 1. O 2y - e + +In=C

A: To solve given differential equation

Q: зхе-МХxcos(Nx) 5- a. Differentiate: y = M csc(Nx)+Nx

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Q: y y" – (y')? = 0 where * = y'. If consider dæ u = y', then the D.E. is reduced to (A) Y dy du u? (B)…

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Q: If y =Aex +Be™ d'y -(m+n) dy. Show that + mny = 0 dx

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Q: 3 13. If x = u + v³ and y = uv – v² are solved for u and v in terms of x and y, evaluate ди ди dv dv…

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Q: u= In(x² +y² +='), x=rcos0, y =r sin 0, : =r= (1,0) =? O a. 1 O b. T/2 O .0 O d. -1 O e. 2

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Q: 1 Evaluate dV, where E lines between the spheres a2 +3? + 22 = 1 and E 22 + y2 + z2 = 9 in the first…

A: Solution

Q: xyz dV, where E is the rectangular box E = {(x, y, z) : –1 < x < 2,0 < y < 1, –3 < z< 0}.

A: ANSWER:

Q: Given y = Va In æ , what is dy dr In z+2 In z+y7 dy dr dy dr In z-2 dy In z-I dr ||

A: Given,

Q: Using the approximation dy dy * Yn+1 - Y, and that dr 1, y = 2 dr h when r= 0. Then, y, = A h-2 h+2…

A: Use the approximation hdydxn≈yn+1-yn and that dydx=1, y=2 when x=0. Then y1=?

Q: 2. Compute ¡ E x dV , where E “ tpx, y, zq | x ď 0, z ď 0, x2 ` y 2 ` z 2 ď 9u

A: The given integral,

Q: dy e, solve the IVP = 40 dt 5y y(0) = 10. - %3D 100-4t cag

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Q: 4. Use Green's Theorem to evaluate | ay dx + (1 – ry) dy where C is shown below y (14) F1,2), (1.1)…

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Q: What will be the value of (h, k) in the given DE: * (x – 2y + 1) dx + (4x – 3y – 6) dy = 0 | h = 3,…

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Q: dw If w = f(x, y, z) = In(x² + y? z?),x = cost y = sin t ,z = 4VE , then is : dt %3D %3D

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Q: dy 3. da + y = 2xy?e"

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Q: dy dx If y=e+19 then O 19e+19 O 4er+19 O 57er+19 O 3er+19 2er+19

A: Please see the answer in Step 2

Q: 14. Evaluate 4y dx +3ax dy, where C is the trapezoid with vertices (0,0), (2,0), (6,2) and (0,2).

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Q: 15- dy _y* -x diferansiyel denkleminin genel çözümü aşağıdakilerden hangisidir? 2ху dx x-y' =cx 046…

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Q: Given x²y3 = In(xy) Show (using complete solution) if the equality below holds dx (x\(3x²y3 – 1) dy…

A: Using differentiation

Q: u2-1 Given y = dy and u = Vx2 + 2, find dx %3D u3+1

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Q: E(z, t) = ex cos(@t – kz + Þ1) + ey cos(wt – kz + $2) = €;E× +e,Ey %3D

A: Consider the given equation: Where,

Q: 6. If z2 = x2y2 (where x, y, and z are positive), and dz then what is when x = 2 and y = 3, given…

A: Given problem:- If z2 = x2 y2 (where x, y, and z are positive), and dz/dt then what is when x = 2…

Q: 1. Evaluate a dV where E = {(x, y, 2) E R³ | 0 < z < x + y,0<x < y?,0 < y< 1}.

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Q: Arrang e linear form: dy + Px)•y= Q) in ov dx (16 + 2+)dQ =[4(10+zt)- 20]dt

A: The linear form of differential equation is: dy/dx + P(x) . y = Q(x) Or dx/dy + P(y) . x = Q(y)