(1 point) Evaluate the line integral y dx + x dy where C is the parameterized path x 1 x = t², y = t³,2 ≤ t ≤ 6. foydx + x dy=

Q: Classify all level curves of f(x, y) = Vy² – x² and draw its contour map.

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Q: b) Evaluate S(2y + 4z)dx + (2æ + 3z)dy + (4x + 3y)dz, where C is the curve given by r(t) = for 0 <t…

A: given ∫C2y+4zdx+2x+3zdy+4x+3ydz where C is the curve given by rt=t3,2sinπt2,3cosπt2 for 0≤t≤1…

Q: Find the length of the curve y = e + e for -1 ≤ x ≤ 1.

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Q: Usethemethodofundeterminedcoefficientstofindthecompletesolutionsofthefollowingdifferential equations…

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Q: Question 2 Find the minimum value of (x.y)=2xr+4y on the curve x^2+xy+y^2=16 Select one: а. -18 C b.…

A: Given, fx,y=2x+4yx2+xy+y2=16         let gx, ygx,y=x2+xy+y2-16

Q: 2. Evaluate f (x^²y³ − 2y)dx + (3x + x³y²)dy where is the curve given below oriented in clockwise…

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Q: The value of the line integral fydx + xydy over the straight-line path C from (0, 0) to (1, 2)…

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Q: -3. 3) to the curve given by f(x) =

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Q: Which point on the curve y = Vx – 1 + 8 is closest to the point (5, 8)? (x, V) = ( What is this…

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Q: Evaluate S xy dx + (x + y)dy along the curve y = 2x² from ( − 3,18) to (-2,8). с Sxy dx + xy dx + (x…

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Q: Prove that there no line through the point (0,1) is tangent to the graph of y = x*.

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Q: 3. Show the limit x+y lim (x,y)-(-1,1) x+1+iny does not exist.

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Q: Draw the level curves of f(x,y)= x² + 9y² for k=0, k=1, k=9.

A: Given curve is, fx,y=x2+9y2

Q: Find the length of the curve x=t/(1+t),  y=ln(1+t) ,0≤t≤2

A: Given curve x=t/(1+t), y=ln(1+t) ,0≤t≤2. Now we have to find length of curve as shown below

Q: 4) Evaluate (¹ + tany)dx + xsec²ydy where C is the curve Y=X²-1 from (1,0) to (2, 3)

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Q: (47) Let C be the curve y = 5x where 1 ≤x≤9. Calculate the length of C.

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Q: V 25t* – 1 dt with 4 < x < 6. Find the length of the curve y = 1 - Length is

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Q: uppose that x + y = 2. What is y" at the point (1, 1)?

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