If a curve C is given by r(t) = (21,3t), what is |r'(t)|? (Type an exact answer, using radicals as needed.)

Q: (b) Verify that Green's Theorem is true for S,3(y² – x) dx + (x² – y)dy given that the curve C is…

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Q: (b) Investigate where the curve y = xy4 - x² is concave up and concave down?

A: Given curve is y=x4-x2 find the concavity of the given curve

Q: If the curve I=3+ at? y= at + bt has a tangent line y=r-4 at t 1, what is a+b? %3D

A: We have to find a+b

Q: = V4 cos" : – 1, y = 10 < x < 30

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Q: 1. Find the equation of the tangent plane to the given surface at the point (0,-1,-2). * 2r2 „2

A: by using formula of plane

Q: 3. What is the length of the curve r = cos3 (-) where 0 < 0 <- 4

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Q: 1 Find the exact length of the curve: r(t) = , 6.

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Q: 1. Consider the curve C given by y = 5 + 2x3/2, 0 < x <1. (a) Find the length of the curve C.

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Q: (B) The length of the curve r(t)=(1+1)i+(1-1j+r/2k from the point t=- to the point r= is 2. -IN

A: The length of the curve means the arc of the length of the curve . The arc of the length of a curve…

Q: Find the exact length of the curve. = 플Vy (y-3), 4sys 16 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: Find the arclength of the curve y = (x² − 4)² on [2,4].

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Q: Given the curve y² = 5x – 1 at point ( 1,-2 ) , find the equation of tangent and normal to the…

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Q: Find the exact length af te of the curve, 2. x-

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Q: Find the slope of the tangent line to the parametric curves x=3t+2, y= 2t^2+ 3t-3 at t=11 and then…

A: The given question as belonging to the derivative in which we have to find the derivative or the…

Q: Find the arclength of the curve y = * - In x if < y s-1. Do not simplify your answer for this…

A: Given: y=18x2−lnx18≤y≤e28−1

Q: 10. Find the exact length of the curve y = In(sec x),0 < x<T/4 %3D

A: This is a problem related to integration of the function. Based on the integral formula we will find…

Q: 2. Find the arc length of the curve y= from x-2 to xD3 16 2x2

A: The solution is given as

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: If lx + my = 1 touches the curve (ax)" + (by)" = 1, show that %3D )+) = 1.

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Q: a) Given a curve y = px* + 2x has turning point at (–1,q). Find the value of p and q.

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Q: y = e*, 0<z<1.

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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: Find the exact length of the curve y = In(1 – x²), 0 Sx S

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Q: Find the exact length of the curve. y = In(sec(x)), OsxSa/4

A: Length of a curve f(x) in interval [a,b] is given by ∫ab1+(f'(x))2dx

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

A: The solution for the above question is as shown below.

Q: Find the length of the curve y = V- from z =1 to r = e. 3

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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: The length of the curve y = Ey3/2 between x = 0 and X 1 is %3D

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Q: Find the exact length of the curve. y = In(sec(x)), 0<x< 1/3 In (2 + v 2 ) – - In (1)

A: Since you have posted 2 questions we will solve one for you please resubmit the question. Given:…

Q: (11) Find the tangent line(s) to the parametric curve given by * = t5 - 4t3 y = t2 at (0, 4)

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Q: Find the arclength of the curve y = x – In x if < y< -1. Do not simplify your answer for this…

A: Given: y=18x2−ln⁡x if 18≤y≤e28−1 ⇒f(x)=18x2−ln⁡x if 1≤x≤e The arc length of the portion of the graph…

Q: (b) Verify that Green's Theorem is true for S,3(y² – x) dx + (x² – y)dy given that the curve C is…

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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: Find the exact length of the curve. y = In(cos(x)), TC 0 < x<.

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Q: Find the exact length of the cur curve. y = Vx- x2 + - sin (V)

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Q: Find the length of the arc of the curve x2 + y2 = 64 from x = -1 to x = -3, in the second quadrant

A: The curve in the second quadrant can be represented as, x2+y2=64y=64-x2   The derivative of the…

Q: Let Sketch the curve and find the length of this curve. r(t) = (t, 3 cost, 3 sin t), 0≤ t ≤ 2π.

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Q: Starting from the point (2, –1, 2), reparametrize the curve r(t) = (2 – 2t, -1+ 2t, 2 – 3t) in terms…

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

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Q: Find the arclength of the curve y=3/2x^2/3 for x=1 to x=8.

A: Find the arclength of the curve y=3/2x^2/3 for x=1 to x=8.

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

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Q: Find the exact length of the curve. y = In(sec x), 0s x s a/3

A: This question is based on application of Derivative.

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: 3) Find the exact length of the curve. y = In(cos r), 0 < x<

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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.