Given that the line y =r- b is an asymptote to the ar curve y a,b €R,r = 1, then b = I-1 -1-a B 1-a a +a D -1+a

Q: (a) find a parametrization of the path C, and (b) evaluate (r? + y?) ds.

A: Here we have to find the Parameterization of path C, Counterclockwise around the circle x2+y2=1 from…

Q: Find the length of the curve given by c(t) = (t*, t², tº), for t E [0, 1].

A: Given:- C(t) =(t4 , t2, t0 )  To find:- Length of curve [0, 1]

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: Q4) In simple circular curve ,the external distance (9.71m ),the middle distance (9.02m) and stat…

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

A: We have to solve the given integral by Green's theorem.…

Q: If C is the curve |z| = 3, then cos(z) -dz .3 O - Tİ Ο 2πί 1 O none of these

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Q: Find the length of the curve described by y = V sec* t – 1 dt, - sI 4 4 (a) 4 (b) (c) (d) 2/2 (e) 1

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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: If C = {(x, y): 1 ≤ x ≤ 2, y = ln(x + √x² − 1)}, find the length of the curve. -

A: C=x,y: 1≤x≤2, y=lnx+x2-1

Q: Let C be the curve in space given by the following parameterization. Then d + 2dy +adz is equal to…

A: Given ∫xdx+2dy+zdz = ∫(xi+2j+zk).(dx i + dy j + dz k) = ∫F.dr Here F = (xi+2j+zk)…

Q: Compute f ds for the curve specified. f(x, y, z) = 2x2 + 8z, c(t) = (e*, t², t), 0 sts 1

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Q: For a χ2-curve with 22 degrees of freedom, find the χ2-value that has area a. 0.01 to its right. b.…

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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: Given the path C that is the line segment from (-4; 0) to the origin, and the curve y = 2x² from the…

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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)=<21/2ti+etj+e-tk>. The given limits of t are:…

Q: Let C be the curve y= 3ln(9-x^2), [-0.9,2.9], find the arc length C.

A: Given y=3ln9-x2 ,-0.9,2.9

Q: 1. Show that the curve a(t) = (t,t² + 1, t – 1) is regular.

A: We’ll answer the first question since the exact one wasn’t specified. Please submit a new question…

Q: Consider the curve r (t) = (t, tº, tº) ; t > 0 Does the point (1, 1, 1) belong to the curve and if…

A: Please refer the attached image for complete solution.

Q: If a curve C is given by r(t) = ⟨t, t2⟩ , what is | r'(t) | ?

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Q: 7. Given that the line y = r -b is an asymptote to the ar curve y a,b €R,rz 1, then b = A -1-a 1-a C…

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Q: Compute the length of the curve over the given interval. r(t) =〈3t, 4t − 3, 6t + 1〉, 0 ≤ t ≤ 3

A: Given rt=3t,4t−3,6t+1,  0≤t≤3Formula→Arc length=∫abr't dtr't=f't2+g't2+h't2    rt=xt,yt,zt

Q: r(t) = 6ti + 3/2ťj+2¢k, 0<t<1

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

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Q: By using Green's theorem evaluate (4.ry – y') dr + (x + 3ry) dy where C is a closed curve starting…

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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: To give the first digit x the second digit y, three points are given as follows: (0, 0), (ax, ay),…

A: The given points are 0 0 ax ay bx by

Q: Given F(x, y) = [arcot(/K)-(secx)* - 2y]i+ 3x-es 2021 evy and the curve C=C,UC,UC, as shown in the…

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Q: Find the length of the curve given by c(t) = (t*,t²,tº), for t E [0, 1].

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Q: 1. Let y be the part of the curve y =r² running from (-1,1) to (2,4). Calculate ry dr + (x+ y) dy.

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Q: (b) Suppose C is a curve of length N, and ||F|| < M, where M is some positive number. Prove that F.…

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Q: The length of the curve that results from the intersection of r = 1,0 <0 < T,0 < ¢ < 0.5n, with 0 =…

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Q: Evaluate [ f (x,y,z) ds given that f(x,y,z) =, and the curve C is ř(t) = 2ti +t²j+÷tk (1<t<∞) %3D…

A: Given: f(x,y,z)=x2xy+6yz r→(t)=2t i→+t2 j→+13t3 k→   1≤t&lt;∞

Q: A circle of radius a in the xy plane, centred at the c is described by T = ¢ +acos (t) i +asin (t)…

A: In this question, we need to change the orientation of the path.

Q: 1. Find the exact length of the curve. (a) y² = 4(x+ 4)°, 00 (b) y = In z, 1<I<2

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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: |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: Let C2 be the curve defined by R(t) = (t² +t + 3, 4t – 5, 2+ t – t2), t e [0, 1]. %3D | (x + y+ 2)…

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Q: The arc length re-parameterization of the line l: F(t) = (1,1, 1) + t(1,2, 3) with 0 <t < 1 is given…

A: This is a problem of curve parametrization.

Q: Let C be the curve given by: r(t) = 3costī – 3sintī + (3t + 1)K,0 < tsTV2. Then length of C is: O 6n…

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Q: for the curre y=: f(n) = n*, 0 sM 32 find the curve'slength given by: 1. 2 It dn

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Q: The arc length function for the curve r(t) = (3e' , 2, 4e*), 0 <t< 1, is s(t) =

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Q: let rit)= demti+ dsintf+? Find the length of this curve from t=0 to t = 4.

A: we have to find the length of the curve

Q: )مه و و ي (x2 + y?, y* + 4x) · dr (2,1) )هد0( )ه,(

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Q: Find the length of the following​ three-dimensional curve.   r(t)=2+3t,6−2t,−8+7t​, for 1≤t≤6

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Q: The value of f. ydx + zdy + xdz where C is the curve x = y = z = 2t? from t = 0 to t = 1 is

A: Here we have to find the value of ∫cydx+zdy+xdz where C is the curve x=y=z=2t2 from t=0 to t=1.

Q: ind the orthogonal trajectory of the curve y? = ax²(1- cx); with a held fixed.

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Q: Use Green's theorem to find the k number that satisfies (k + 3) ∫C((k/2)*(x^k)*(y^2))dx + ((yx^(k +…

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Q: Given that the tangent and normal to a curve at point P(x, y) meet the x-axis in A and B…

A: 1st we will form a differential equation from given data and then solve it to get the curve

Q: The tangent line to the graph of y = In(2x) is perpendicular to a + 4y = 1 at the point where Select…

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