Consider the curve y = zy+1. What is the value of- dz at (0, 1)? None of the given choices

Q: I Find the acute angle between the two curves xy = 3 and x2 = 9y

A: Given data: First curve xy=3. Second curve x2=9y.

Q: The length of the curve defined parametrically by: x = e*cost, y = e' sint, 0 Sts is equal to:…

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Q: = V4 cos" : – 1, y = 10 < x < 30

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Q: Set up an intergal of the Curve for the length 3T Y%3DZE* sin (x), O4 xE 2

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Q: Consider the parametric curve x = Vt , y= 3t –1, for t20. Find the slope of the tangent line to this…

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

Q: 3 The arc length of the portion of the curve y =x² with 0<x<4 is

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Q: Find the arc length function for the curve  y = 2x3/2  with starting point P0(1, 2).

A: Arc length is a distance between two point along the section of a curve.

Q: Determine the Arc Length of the Curve. x=(2y3/3)+(1/8y) for 1≤y≤2

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Q: Find the length of the curve x = e' cos(t), y = e' sin(t), 0 <t < r. Length =

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Q: Calculate F.dr, where C is the curve given by ti + 123+ tk, with t = [0, 1] and F(x, y, z) = 4xei +…

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Q: The length of the curve determined by equations x = t² and y = t from t = 0 to t = 4 is %3D %3D %3D…

A: The objective of the question is determine the length of the curve.

Q: Consider the curve defined by xy + y2 = 21 Determine dy/dx for this curve at the point (4, 3)

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Q: Show that the exact length of the curve below is y = Vr - r² – sin ¬1 (V7)

A: SOLUTION-

Q: d'y Consider the curve y = ry+ 1, What is the value of at (0, 1)? dz

A: Given curvey2=xy+1

Q: Sketch the curve by eliminating the parameter, and indicate the direction of increasing t at t = 0.…

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Q: Find the length of the curve. Vzti + e'j + e-tk, 0 sts 3

A: Given data:     The given expression is: r(t)=&lt;21/2ti+etj+e-tk&gt;. The given limits of t are:…

Q: Set up an intergral for the length of the curve, 04X y%3DZE* sin cx), O4 XE

A: Explanation of the answer is as follows

Q: Find the tangent line(s) to the parametric curve given by a = t5 – 4t3 y = t? at (0, 4).

A: Find the tangent line(s) to the parametric curve given by x = t^5-4t^3 , y = t^2 at (0,4).

Q: Find the length of the are of the curve п x=e' sint , y=e' cost from t-0 to t=:

A: Given: x=etsint, y=et cost from t=0 to t=π2

Q: 5. Find the length of the curve given by y= Vt* – 1 dt and 1<x<2.

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Q: Find the arclength of the curve r(t) (6 sin t, 2t, 6 cost), -2 < t <2

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Q: Compute the length of the curve given parametrically by x=1/3t^3 and y=1/2t^2 for 0 less or equal to…

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Q: What is the formula for the slope dy/dx of a parametrized curve x = ƒ(t), y = g(t)? When does the…

A: Given parametric curves are

Q: Find the arc length of the curve on the given interval. Parametric Equations    x = 6t2 , y = 2t3…

A: Given parametric equations are x(t)=6t2, y(t)=2t3

Q: Find the length of the curve x=cos^2t, y=sin^2t, 0≤t≤Pi.

A: In this question,we find the arc length of the curve using x=cos^2(t),y=sin^2(t),0&lt;=t&lt;=pi Arc…

Q: Find the length of the curve x=1+2sin at, y=3–2 cos at, 0<t<l

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Q: where C is the curve r(t) = (sin(t), cos(t), sin(2t)), 0 ≤ t ≤ 2

A: Given C is the curve                        r(t)=sin(t), cos(t), sin(2t), 0≤t≤2π and…

Q: Find the exact length of the curve. y = ln(cos x),   0≤ x ≤ π/3

A: Formula used: L=∫ab1+dydx2dx

Q: The length of the curve defined parametrically by: x = e'cost, y = eʻsint,0 <t <, is equal to:…

A: given parametric curve x=etcost     y=etsint

Q: Find the length of the arc of the curve having the parametric equations x = t³ and y = 2t2 from t =…

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Q: 3 The arc length of the portion of the curve y=x 2 with 0<x<4 is

A: I have append the formula used to find arc length in the solution part.

Q: Find the tangent line(s) to the parametric curve given by a = t¹ - 9t² and y=t² at (0, 9).

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Q: The parametric curve x(t)=t−2t6 and y(t)=t7+2t2 is given. In which case is the tangent line at the…

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Q: Find the arc length of the curve y = (ex + e-x)/(2), 0 ≤ x ≤ 2.

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Q: Find the length of the curve y = ln (sec x), 0 <I<÷.

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Q: Can there be a curve satisfying the following conditions? d2y/dx2 is everywhere equal to zero and,…

A: To check: The curve satisfying the given condition or not.Explanation:

Q: For the curve x=3cos(t), y=4sin(t), find the value of d^2y/dx^2 at the point where t=π/5.

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Q: Find the length of the arc of the curve having the parametric equations x = t³3 and y = from t = 0…

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Q: Consider the curve x²y + y²x = 6 A) Find in terms of x and y dx

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Q: Find the equation of the tangent line to the curve y = et at the point (0, 1). Give your answer in…

A: Given,            The curve is y=exx2+1 and the point is 0,1.To find : Find the equation of the…

Q: Evaluate + 5x)dx + (ye* – 3y²)dy where C is the boundary of the curve given below. -2

A: Detailed explanation mentioned below

Q: Calculate the length of the curve γ (t) = (cos(2t), sin(2t)) t ∈ [0, π].

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Q: s to the curve y = x* at the %3D

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Q: py*(1 + x*)dx + 2ytan xdy ,where C is closed curve xi +yi = 1

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Q: Find the lengthof the curve r= a sin (0/2), 0s 0S T, a>0

A: The formula for finding arc length is L = ∫0πr2+ drdθ2dθ, where r = a sin2(θ2)

Q: Consider a curve parameterized by: c(t)=(sin^3(t),cos(t)) Compute dy/dx at the point ((sqrt(2)/4),…

A: Differentiate the given function as follows.