5. Suppose curves C₁ and C2 are parameterized as follows: C₁: (x(t), y(t)) = (0, t), and -1 ≤ t ≤1 C2: (x(t), y(t)) = (t², t), (a) Sketch C₁ and C₂ with arrows showing their orientation. (b) Suppose F = [x+3y, y]. Find feF. dr where C = C₁ + C₂. 0 ≤ t ≤1

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A: (a) Equation of line L1 is y=-x-2 (b) Equation of line L1 is y=x+8

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A: Please see the below picture for detailed solution.

Q: 8. The rectangular function is defined by: A, (0) - {₁ T - sts Plot the following rectangular…

A: All the graphs are plotted below.Explanation:Here are the plots:

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Q: What curve is described by the function (t) = (2t + 3) + i(t - 5), 0 ≤ t ≤ 1

A: Step:-1 Given parametric function is ft =2t +3 +i t-5,  0≤t≤1 Here,  x=2t +3  ---(1)y=t-5  ---(2)…

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A:

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A:

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A: Given y=ax3+bx2+cx+d

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A:

Q: 5. Evaluate - xy+3z)ds where C is the line starting at (1,1,1) and ending at (-1,-2,-3).

A:

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A: NOTE: Refresh your page if you can't see any equations. . the given tangent line is  here we have…

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A:

Q: 5. Suppose that you were standing at the point (-1,2, 39) on the graph of f(1,y) = r -3ry+4y. If you…

A:

Q: Which of the following defines an equation of a plane curve that does NOT have a vertical asymptote?…

A: Given:  We have to find the equation of plane curve which has no vertical asymptote.

Q: 2. A curve is defined by f(x) = a√√x+b, where a and b are constants. the point (4, 6), determine the…

A:

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A: Tangent is horizontal where derivative is zero

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Q: a) Given that straight line y + x=2 is tangent to the curve y =x² – 6x + q. Find value q.

A: Given,  y+x=2⇒y=-x+2

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