r(t) = 6ti + 3/2ťj+2¢k, 0

Q: 48. x = e' – t, y= 4e"², 0<t<2

A:

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: 7) Find the exact length of the curve. x= e' +e', y =5-2t; 0<t<3

A: Solution:Givenx=et+e-t     y=5-2t     0≤t≤3To find the length of the curveFormula:Length of the…

Q: Find the exact length of the curve. y = 5 + + cosh(6x), 0 < x < 8 6 31

A: We have to find exact length

Q: Find the exact length of the curve. y4 1 X = 8 1sy< 3 4y2"

A: Here the formula of length of the curve is:

Q: 13- Find the length of the curve a) r(t) = 4costi + 4sintj³ + 3tk³ 0< t < 3n b) r(t) = 4ti + 4tj¬ +…

A: Please refer the image,

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

A:

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

A:

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 length of the curve: 7= Scos 4. t2.

A:

Q: Find the exact length of the curve. = 플Vy (y-3), 4sys 16 3

A:

Q: 1 use the formula L= [, ct to find the length of the curve 1 X=-ť. y = 1 for 0St<1

A:

Q: 4. Find the length of the curve 7(t) = (t2,,t³,t) for 0st<4

A:

Q: Find the length of the curve given by ř () = (6t, 12/T, 3Int) for 1<tse. O 8e-4 O 2e-1 O 4e - 2 O…

A:

Q: 64. Find the length of the curve y = 1 - e",0 SISI.

A: Formula to find the length of the curve helps to find the required length. Formula to find the…

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

A:

Q: 3. Find the length of the curve r = e® for 0ses 2n.

A: Given polar curv er=eθ   ; 0≤θ≤2π

Q: Find the length of the curve given by x(t) = 1 + 3t² ,y(t) = 4 + 2t³, 0 <t < 1.

A: xt=1+3t2yt=4+2t3 Differentiate the above equation w.r.t."t"…

Q: Find the length of the curve. r(t) = (4t, 0 <ts 1

A:

Q: a)Find the exact length L of the curve 3y = (4x – 3), 1 0. Answer: b) Evaluate xe*dx Answer: .3 c)…

A:

Q: compute the length of the curve over the given interval. r(t) = 2ti − 3tk, 11 ≤ t ≤ 15

A:

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

A:

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

A: Finding r'(t)

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

A:

Q: Find the exact length of the curve. 1 1sys 2 4y2' X =

A:

Q: 9. Find the length of the curve defined by r(t) = (t, -1sts1.

A:

Q: Find the exact length of the curve. 1 + 1sys 2 8 4y2

A:

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

A:

Q: Find the length of the curve r(t) = (1,t2, t³). 0<t < 1.

A:

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

A:

Q: Find the length of the curve r= e2θ, 0≤θ≤2

A:

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 curve. Vzti + etj + e-tk, Osts 3

A:

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

A:

Q: The length of the curve defined by x =(v² + 2)E, y € [0,1]. Select one: none O 12

A: Arc length of the curve x=g(y), y∈[a, b] is, S=∫ab1+(g'(y))2 dy

Q: Find the length of the curve. 6t, , r(t) 0 <t< 1

A: Given:-r(t)=6t, t2, 19t3,         0≤t≤1since we have to find the length of curve.

Q: 3. For the curve x – xy² = 8e²4, do the following | a) Verify that the point (2,0) is on this curve.

A: Given, curve x3-xy2=8e2y

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

A:

Q: 7. Find the exact length of the curve: x (t) = 2t, y(t) = 2t, 0 ≤ t ≤ 1

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: Find the length of the following curve (a) x = 2t , y = cos 4t, 0 <t<

A:

Q: Find the length of the curve. 2ti + etj + e k, 0<tS 4

A:

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

A:

Q: Find the length of the curve y = a +; from a = 0 to x = 1. O None 5/2 O6/2 3 O4/2 3. 3

A:

Q: Find the length of the arc of the curve in the given range, y3 1 x = 16y + 4y² + 3 0 <y< 4 - 4(y…

A: we have to find th length of the arc for the given curve .

Q: Find the exact length of the curve. 9 s ys 16

A:

Q: Find the length of the curve. r(t) 4 it2j3k, 0 st s 1

A: Consider the curve x = 4, y = t2 and z = t3.The derivatives are

Q: Find the length of the curve r(t) = for 0 ≤ t ≤ 2π Enter the exact value.

A:

Q: et +e- find the length of the curve h(x) = from r = 0 to z = In 2.

A: The standard formula for arclength will be used in solving this problem. The typeset solution is…