(1) P₁ = 1 k₁ If y is such that ry = ds, then snow that : ( d²p d w² = p +- (ii) σ₁ = 1 T₁ P d²p dy² p+. Rp d R o dp

Q: y= e fonksiyonunun d'y dy 11 + 27y = 27e dr 11z dr?

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Q: (s-14)4 te-14 6 tBe4t 5) 6 t324t =) 6 a) then the function f(t) can be: 82 +58 + 14. 8 7 31 s²+ } 8²…

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Q: (b) If z r+ry- y7, 1= u+ and y = 2uv, find: in terms of du %3D u and v.

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Q: y² + 1 dy (y – 1)²(y + 1) 1.

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Q: 18. The drawing on the right shows a tangent drawn to a circle at the point P(x; y). Write down the…

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Q: x dx+ y dy=x²ydy– y²xdx Choose. dy х-у+xtan 2 dx Choose..

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Q: SOLVE the ff. D.E. 2 1.) x² y² = 4x² + 7 xy + 2y ² ļ CONSIDER THIS D.E. 2xy-3y2 (6x + y²) dx +…

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Q: Evaluate the value of I = (4,0). I = Sleby. r 3x) dx + (6xe6y + y)dy, where I is the straight line…

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Q: Q3: if it was A(x, y, z) = x?yi + y?zj + z?xk and Ø(x,y,z) = xy + yz + zx find (a) A. (VØ) (b) Ø…

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Q: Evalwate f, the inaicated point. (Y.y) and Fy y,y) CY.y) at 3. at (l,3)

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Q: Q1/ If z = f(x, y) and z* - y? = 6x²y°z7 Find: and dz

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Q: Evaluate . y? cos(x) dx + 2ysin(x)dy where C is the straight line between (0,0) and

A: The equations of the straight line joining (0,0)to π2,1 are x-0π/2-0=y-01-0=t(say) i.e. xπ/2=y1=t…

Q: HW If r(H)=6 sin zt ċ+ 6cas ztj + 5tk find T,Ñ, V, a and speed at t-2

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Q: Evaluate I = f (sin(x) + 2y) dx + (7x + 6y) dy for the nonclosed path ABCD in the figure. y D =…

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Q: If Sf(x)dx = 5, i f(x)dx = 2, and Sif(x) dx = -1, find f(x)dx. %3D %3D А.) -2 В.) 2 С.) -3 D.) 3

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Q: the diagram: ΔLMNΔLMN  is a right-angled triangle with vertices L(−6;7),M(a;b)L(−6;7),M(a;b) and…

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Q: c). Evaluate √√x² + y² ds along the curve r(t) = (4 cost)i + (4 sint)j +3tk, -2x≤t≤2π.

A: We solve the given line integral.

Q: Find the general solution using substitution of each of the following DE: 1.) (2x + y + 6) dx + (2x…

A: As per our guidelines, we are supposed to solve only first question. Kindly repost other question as…

Q: 3) 2 y dx + (x - x³y²³) dy

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Q: dw 21. : 1-cosw A. -tan w + secw + C B. w – cotw + C C.-cotw – cscw + C_ D. -cscw + tanw + C

A: We can find the integral value as below.

Q: af af and for dy 5. Find f(1, 9) = 1+2² + y²"

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Q: where Dx = X₁-X₂ and Dy = |Y₁ — Y2]. Assume that the two locations are independent and uniformly…

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Q: $ x4* dx + 2x*y dy where C is the triangle wl vertices (0,0), (3=), and (2, 4) i ?

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Q: If u = x²zî + yz?j – xyk and 0 = x²yz then find the value of u. (To)

A: Consider a function fx,y,z. The gradient of the function can be defined as, ∇→f=∂f∂xi^+∂f∂yj^+∂f∂zk^…

Q: Say whether the Runction is even, odd, or neither. Give reusans for your dnswer. go0 = x"+x-1

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

Q: d²y and dx2 Find dy then simplify whenever possible. dx 1) y = 3t5 – 2t x = 4t3

A: Note:- Since you have asked multiple question As per our policy, we will solve the first question…

Q: Given z = f(x – y, 2x – 2y, 3x – 3y). Show that dz dz 0. dx fie +

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Q: If x2 z2 + y² + xz3 = 3, then dz at the point (1, 1, 1) is: O b. Ос. - 3 d. - 3 Ое. f.

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Q: 1. Decide whether the folloring stabe ments ae false . Justify true or (a) YxeTR, ¥yeR, x²-y² z xy…

A: 1. a ∀ x ∈  R, ∀ x ∈  R, x2+y2 ≥ 2xy  TRUE. Because,  ∀ x ∈  R, and ∀ x ∈  R we have (x-y)2 ≥ 0.…