4.34 Show that KT 1 - t2 + t 4.35. Show that the curve x =te, + e3 lies in a plane. t 11 o anoldo ut moia1ot baa enia wW ejermas en Find the most general function f(t) so that the curve &B aq isx = alcos t)e, X A 36

Q: 3) Consider the curve C in R³ given by: r(t) = (t + In t, t – In t, 4t'/²) con 1<t< 2 An expression…

A: Formula: If r(t)=x(t), y(t), z(t), a≤t≤b is parametrization of a curve C then the line integral…

Q: Find the length of the curve y = -9+4x3/2 over the interval 0 <x <1. OAZ= (1/54) 37 /37+1 CO B I =…

A:

Q: *Gl0/ Apply Stoke's theorem to Cal cu late S4y dx +2zdy + 6y dz where c i$ the curve of xyt 2 = 6z…

A: Apply Stokes theorem to calculate ∫C(4ydx+2xdy+6ydz) where c: intersection of x2+y2+z2=6z and z=x+3…

Q: (3) Compute f ds over the curve specified. (a) f(x, y, z) = 2²,r(t) = for 0 for 0 < t < 1

A: Consider the equation

Q: a bounded by the curve y = 3VI and the lines z = 6 and z= 8 above the z – azis is Võ+ 12v6 O 10

A: We have to choose the correct answer

Q: dr. Let f(z) =z. Find from z-0 to Z-4+2í alongthe curve C given Z=21 to z=2i

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Q: 1 - Findthe lenght of the Curve a) r(t)* = (3cost)i³ + (3sint)j* + 4tk¬ for 0 < t < 2n b) r(t)* =…

A: Use formula of length of curve

Q: 3) Find the exact length of the curve: x = y = In(1+t); 0<t<2.

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Q: 12 sin°(z) dr: C is any closed curve -dz enclosing 7/6 (a) Ic 6z – T -

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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: 2 32 |for 1st<3. length of the curve c(t) =| In t,-t"

A:

Q: Which of the following functions parametrizes the portion of the curve x=y³-4 that starts at (-4,0)…

A: In this question , we can check one by one all option .

Q: 13.3. Let y be the curve given by z(t) = t + it?, 0<t < 2T. Evaluate |z|²dz.

A:

Q: Let C be the curve in space given by the following parameterization. r(t) = tỉ + t²j + 9k, 0 < t s…

A:

Q: 3. Below is a curve C, which is the intersection between the surfaces S: z = 4 -x? and S2: z + 2x…

A:

Q: 3. Below is a curve C, which is the intersection between the surfaces S1: z = 4 -x? and S2: z + 2x…

A: A is the correct answer.

Q: 11. Evaluate the line integral F dr where F (x,y) = xy'i+vi and the curve C is the shortest path…

A:

Q: The value of le ydx + zdy + xdz where C is the curve x = y = z = 2t2 from t = 0 to t = 1 is A В 15 C…

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Q: 6. Find F' and dF[a; h] where: In ¤1 (a) F(x1,x2) and hence show that if v is tangent to the curve…

A: (a.) Given: Fx1,x2=lnx1x2e2x1x22cosx1 To find: F' and dFa;h To show: If v is tangent to the curve…

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: 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: Compute I = (2x²132²y+ 4xy)ax +(x'+2x²-y') dy+zdz along The curve C C4U Cz UG given in the figure…

A: Given To compute I=∫C2x3+3x2y+4xy.dx+x3+2x2-y2dy+zdz along the curve C=C1∪C2∪C3 given in the figure.

Q: compute the length of the curve over the given interval.  r(t) = (2t2 + 1, 2t2 − 1, t3), 0 ≤ t ≤ 2

A: Length of a curve is also like computing distance between two points but with the restriction that…

Q: Let C be the curve in space given by the following parameterization. r(t) = tỉ + t²j+ 7R, 0 st s 3.…

A:

Q: 6. Let a curve be parameterized by x = t³ – 9t, y = t+ 3 for 1 < t< 2. Find the ry coordinates of…

A: Given that

Q: Consider curve C at R parameterized by: r(t) = cos(2t) î + tf+2 sin(2t)k, with 0 stsT An expression…

A:

Q: Find the work done by F = xyi+yj - yzk over the curve r(t) = ti + t²j + tk, 0≤t≤1

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Q: Let F = e'i+(xe' -e')j- ye'k and cbe a smooth curve defined by Then the value of the line integral…

A: The formula is  ∫F.dr=∫F(r(t)).r'(t)dt Here…

Q: 3.) caiculate S FC().dr, wmere = a:l F=X"ityj;c:Y=1-x?:fromx =1Untix=1 b) Petemine the woru done by…

A:

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: Evaluate F. dr where F = (x – 3y)i + (y – 2r)j and C is the closed curve in the xy plane, x = 2 cos…

A:

Q: c) By using Green's theorem evaluate UTM £ (kry – y") dz + (z² +3ry) dy where C is a closed curve…

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Q: Let m be a positive real number and C be the curve given by: r(t) = mcosti – m(sint + 3)j + (5 –…

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Q: 11. Compute the length of the curve r(t) = (2t, In(t), t²) over the interval 1 <t < 4. (cos(t),…

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Q: (7) A particle moves along the curve 7= (13 – 4t)i + (t? + 4t)j+ (8t² – 3t®)k, where t is the time.…

A: Tangential acceleration is defined as the rate of change of velocity vector where velocity vector is…

Q: 3.5 Given that H = x'a, + ya,, evaluate H· dl, where L is along the curve y = x from %3D (0, 0) to…

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Q: Find the Length L of the curve R(t)= -2cos(4t)i + 2sin(4t) j + t k over the interval [2,6]. L =

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Q: Let a curve be parameterized by x = t³ – 9t, y =t+3 for 1< t< 2. Set up (but do not evaluate) the…

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Q: Find the length of the curve r(t) = (√2t)i + (√2t)j + (1 - t2)k from (0, 0, 1) to (√2, √2, 0)

A: given, r(t)=(2t)i +2tj+1-t2kwe have to find the length of the  given curve from (0,0,1) to 2,2,0

Q: Q() Compute the wark done by F = (2y – x)i + (2z – y)j+ (x-z)k over the curve r(t) = ti + tj+t'k,…

A:

Q: Let C be any curve.

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

A:

Q: 1.108. Find F•dr where F = (z - 3y)i + (y - 2x)j and C is the closed curve in the zy plane, z = 2…

A: We have to find ∮CF·dr where F=x-3yi+y-2xj and C is the closed curve in the xy-plane. x=2cost,…

Q: Compute the length of the curve r r(t) = (2t, In t, t²) over the interval 1 < t < 3 L =

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

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: Ext find the anen of the ragion bounded on the leftby the Curve yx, on the right by the line y and…

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Q: Find the are rength of the curve whose paraumetric equations are : Jfd ad S x=COS2E +2bsin 2t E59 51…

A:

Q: Below is a curve C, which is the intersection between the surfaces  S1 : z = 4 − x2 S2 : z + 2x −…

A: Given that,Below is a curve C, which is the intersection between the surfaces   S1 : z=4−x2  S2 :…

Q: What is the correct piecewise parametrization of a path C created by starting from C₁ of equation y…

A: Concept: We have given the curves  y=x+3x=0 to x=4y=x2 Here the red line represents y=x+3 The green…