Evaluate x ds, where C is a. the straight line segment x =t, y =. from (0,0) to (6,2) b. the parabolic curve x=t, y =, from (0,0) to (3,9)

Q: Find T, N, and B for the curve r(t) = (10t, 10t, e') at (0,0, 1).

A: Given: we have ,

Q: A Curve a with aca) = (2,4,4), 2e2) = (0 ,2 54). %3D %3D Find Kea), B)

A: We will find out the required value for given curve.

Q: d. The curve y= In x , y-axis, the lines y 0 and y 4.

A: Given, We have to find area of region bounded by  y = lnx ; y axis ; y =0 and y = 4.

Q: verify that the given point is on the curve and findthe lines that are (a) tangent and (b) normal to…

A: Given

Q: Find the exact length of the curve. y? = 16(x + 4)3, Osxs 2, y > 0

A: Given data:   The given expression is y2=16(x+4)3. Th given limits of x is [a,b] =[0,2].   The given…

Q: Find T,N and k for the curve:

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Q: Find the length of the curve. r(t) = ( 8t, t², ), 0 <t< 1 %3D 12

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Q: Let C be the curve y = x³ – 3x? + 4x – 1 joining the points (1, 1) and (2, 3). Find the value of…

A: Solving the Cauchy integral using Cauchy theorem

Q: Find the exact length of the curve. x = et – t, y = 4et/2, 0st < 5

A: Find the length of curve:

Q: Find the exact length of the curve. x = et + e-t, y = 5 – 2t, 0 st< 4

A: Given curve: x=et+e-t, y=5-2t We have to find exact length of the curve at 0≤t≤4. Length of the…

Q: Find the exact length of the curve. x = et − 9t,    y = 12et/2,    0 ≤ t ≤ 2

A: Note that:Arc length formula = ∫abdxdt2+dxdt2 dt                   where , a≤t≤b       Given,…

Q: Find the slope and concavity of the curve at the given points. r = 1/u, u = -pi, 1

A: Solution:Given    r=1u, u=-π,1To find the slope and concavity of the curve.Formula:Slope of the…

Q: Consider the curve by given C = C,u Czu Co The uale of r [ zdr + r*dy iS 14 C) 32 B) 15 72 D) - 15

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Q: Find the exact length of the curve. =글Vy (y-3), 16 <y< 25 X =

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Q: Evaluate e fxds, v ds, where C is a. the straight line segment x=t, y = from (0,0) to (8,4) 2' b.…

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Q: Express the curve by an equation in a and y given #(t) = e' and y(t) = 7 – e2. II %3D a) O -a? + y =…

A: Consider the curve  xt=et,yt=7−e2t

Q: Find the exact length of the curve. Vy (y - 3), 16 < y < 25 X =

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Q: Evaluate x ds, where Cis с a. the straight line segment x = t, y = = 737₁1 3' b. the parabolic curve…

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Q: Find the exact length of the curve. y = x3/2, osxs 6 3

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Q: find the eauatjo aof the nor ma l to the curve 2. (x + 3)?y =3y-3x2

A: For any curve y=f(x), slope of tangents and normal at any point x1, y1 can be given by mT=dydx(x1,…

Q: Find a parameterization, x = x(1), y = y(t), tE [0, 1], for the line segment from (2, -1) to (5, 5).

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Q: a) Sketch (hand drawn) the intersection of y? + z² = 25 and x = 3 in 3D. b) Also, describe the the…

A: When two surfaces intersect each other, a new curve is formed. The curve is referred to as the curve…

Q: Find the exact length of the curve. x = et − t,    y = 4et/2,    0 ≤ t ≤ 2

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Q: Evaluate ∫C x ds, where C is the parabolic curve x = t, y = t2, from (0, 0) to (2, 4).

A: Given: Parabolic curve x=t, y=t2 from (0,0) to (2,4)

Q: Find the length of the curve. x=(y - 1) 3/2 from y = 1 to y = 4 O 7 O 10 21 2 O 1

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Q: Find the exact length of the curve. x = et − t,    y = 4et/2,    0 ≤ t ≤ 5

A: We will use arc length formula to solve this questions

Q: Find the exact length of the curve. X = Vу (у — 3), 16 <y S 25

A: First differentiate wrt y

Q: Find the exact length of the curve.42. x = et − t, y = 4et/2 , 0 ≤ t ≤ 2

A: Given eqn : x=et-t,  y=4et/2 ,  0≤t≤2 So, we use dxdt=et-1,  dydt=2et2   Length of the curve =…

Q: Find the length of the following three-dimensional curve. r(t) = (2+5t,9-3t, -6+3t), for 1st≤4

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Q: Q1/ Find the equation of the circle tangent at least to three lines (y = 1, y 5, x 2 and x = 7). %3D

A: We have considered the first 3 lines as the line of the tangents For more see below

Q: Find the exact length of the curve. 36y =(x+4). 5 5 x s 6, y 20

A: Given: 36y2=(x2-4)3,  5≤x≤6,  y≥0 Arc length of curve y=f(x) on [a, b] can be calculated by…

Q: Trace the curve r = sinocos'o. 2)

A: Given: r=12sin3θcos3θ Explanation: r=12sinθcos3θat θ=0r=12sin0cos30=0⇒r=0at…

Q: Find the exact length of the curve given by a = t° ,y (0 <t< 4). Length =

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Q: Find the exact length of the curve. 1 Vy (v - 3), 4 < y< 16 3 X =

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Q: Find the length of the curve r(t)=, -2 "< or equal to" 0, "< or equal to" 2.

A:

Q: Find the exact length of the curve. x = et + e=t, y = 5 – 2t, 0st< 4

A: The solution are next step

Q: nath A = 30, B = 20, C = 11, D = 22. 3. Discuss how to evaluate Z enclosing the origin. dz, where C…

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Q: Eliminate the parameter t to find a Cartesian equation of a curve. x = 1 + 3t,  y = 2-t^2

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Q: Express the curve by an equation in a and y given #(t) = t² and y(t) = 2 t4 + 6. а) x = 4 y? + 5, y…

A: To convert the parametric equation into cartesian we must have to eliminate parameter t from both…

Q: Evaluate x ds, where C is a. the straight line segment x = t, y = from b. the parabolic curve x=t, y…

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Q: 2. Sketch the plane curve by plotting points then indicate the orientation of the curve. x = t2 – 4…

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Q: The siope of a line tangere to the curve y=fx)at(3 4) 0f iz cists) equais

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Q: . Evaluate the length of the curve, y = x/2, from x = 0 to x = 4. %3D

A: first step differentiate w.r.t to x

Q: Explain how to find the length of the curve                         r(t) = ⟨ƒ(t), g(t), h(t)⟩, for a…

A: To Determine: Explain how to find the length of the curve Given: we have rt=&lt;f(t),g(t),h(t)&gt;…

Q: Find the exact length of the curve. y = (1 + x*,3/2, OSxS 5

A: The curve is y=231+x232 , 0≤x≤5

Q: Evaluate the length of the curve y = 2 + Vx , 3 < y< 4

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Q: Find T, N, and B for the curve r(t) = (14t, 14t, e') at (0,0, 1). Hint: After finding T', plug in…

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Q: ² fx ds, where C is с t a. the straight line segment x = t. y = from (0,0) to (16,4) b. the…

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Q: d the exact length of the curve. =√y (y - 3), (y - 3), 4 ≤ y ≤ 16

A:

Q: At what point do the curves r;(t) = (t, 4 – t, 24 + t2) and r2(s) = (6 – s, s – 2, s2) intersect?…

A: The curves are r1(t)=t, 4-t, 24+t2 and r2(s)=6-s, s-2, s2