4. If C is the boundary of a region bounded by x2 + y? = 16 in counterclockwise manner, use Green's theorem to evaluate $ (sin (2x) – y") dx + (sin (2y) + x*)dy.

Q: 4. Integrate: 5dx dx a) f b) [ c) f- 1 dx; d) x' V16-x? 1+ cosx cos x

A: As per our guidelines we are supposed to answer only first three parts. Kindly repost others part as…

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A: Given: f=sinxycosyzcotxz To find: fzyx

Q: Find the derivatives of y with respect to x: a) y = xe* - e* b)' y = e(4x+) e(tx+) X. c) y = e*(sin…

A: Since you have posted multipart question and we can answer three subparts. So, answered first three…

Q: 13. Integrate: S(sec³ 0 tan 0 - sec 0 tan³ 0)d0 A. In sec 0 + C В. In sin @ + С C. sec 0 + C D. sin…

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Q: Find the derivatives of y with respect to x: a) y = xe* – ex b)' y = e(+x+) c) y = e*(sin x + cos x)…

A: Differentiate the function with respect to x.

Q: 7. Integrate: S sec? (n²x)dx A. 2n tan n² + C В. x sec2 п2 + С C.금tan(T2x) + C D. x sec nx + C 8.…

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Q: (b) cos(x² + y²) dy dx where R is the region 9 < x² + y? < 49.

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Q: Find dy/dx by implicit differentiation. 6) x3 + 3x2y + y3 = 8 dy A) dx x2 + 3xy B) dy dx x2 + 3xy x2…

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Q: Differentiate: y = cot(xcsca) = cot x (xcsca - 1) csc (zcsca) Oy = cot x (xcscx +1) csc (xcscx) =…

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Q: the derivatives of y with respect to x: y = xe* – ex y = e(1x+) %3D y = e*(sin x + cos x) %3D y =…

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Q: Let R be the shaded region in the first qudrant shown above. R is enclosed by the y-axis and the…

A: Since you have posted multiple questions but according to guidelines, we will solve the first…

Q: The area of the surface obtained by rotating the curve y = 1<xse about the line x = 32 is ** 12 (32…

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Q: 3) Let F = (y+ev=,8x+ cos(y*)) Use a theorem to compute ſ F •dT where c is the boundary of the…

A: Given that  F→=y+ex,8x+cosy3 To compute ∫cF→⋅dr→ where c is the boundary of the planar region…

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Q: ow the processs on separating the variables of the given DE ich that all terms containing x must be…

A: Remark: A first-order differential equation is said to be separable if dy/dx = f(x, y) , the…

Q: e) S (x² – 2 x + 1)dx

A: According to Bartleby's policy we are allowed to solve only 1 question at a time. Here's the…

Q: sin(2t), y = – cos(2t), z = 4t at P(0, 1, 27) has equation 87 + 2 sin(1). The normal plane to the…

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Q: | | | 8. Given f(x) = sin (4x + 7/7), find f' (Z). a) 0 b) 4 9. The derivative of y = √√ex is: a)…

A: Step 1: Step 2: Step 3: Step 4:

Q: 4) Find the area of the region enclosed by the curves y = sin(x), y = cos (x), X = 0 and x = 2π 5)…

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Q: Let h(x, y) = x5 + y sin²x x² + y² 0, { 25 if (x, y) = (0,0) if (x, y) = (0,0) (a) Show that h is…

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Q: Calculate of of and for the function f(x, y) defined as : ax' dy sin (xy) 1 + y f(x, y) =

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Q: (2) Use Green's theorem to calculate f. F - di for F(x, y) = (x2 + y, e") and C the boundary of the…

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Q: daffəx and åf/ðy y) = x² – xy + y² v) = sin? (x – 3y)

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Q: tion 16 of 17 Let P be the tangent plane to the graph of g(x, y) = 18 – 9x - 18y at the point (4,…

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Q: compute (x2 - 8x +20) dx on the interval (0,1)

A: To evaluate the given definite integral over the open interval (0,1)

Q: /Prove that the value of cos()dz, when z = T + 2i is e + e-1

A: Complex integration of the function

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Q: For F(x, y,z)=(6xsin y+10xz' )i+(3x cos y-4ye"-2y ze" ) j+(-2y'e* +15x²z² )k , find | a function f…

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Q: Find in sin (1 + 2x) + xy = ecosy dy d.x

A: Find derivative

Q: Find a simple closed curve C with counterclockwise orien- tation that maximizes the value of f t* dx…

A: Given an integral. We need to find the C that maximises the value of the integration.  Let's start.

Q: 4. Use Laplace transforms to solve the following initial value problems. (a) y"+2y-3y = 10 sinh 2t,…

A: Laplace transform.