3. Let C be the part of the space curve represented by r(t) = (t, t/², t² +1), where 1

Q: Compute the arc length of the parametric curve given X=1/3t^3-t,y=t^2+3 From t=0 to t=3

A:

Q: Find the length of the following three-dimensional curve r(t) = (9+3t,3 – 7t, – 1+ 5t) , for 1sts6…

A:

Q: Which one is the formula for the arc-length function of a smooth curve r(t) for t>a. ||r" (u)|| du…

A: Given smooth curve  rt for t≥a

Q: Set up an integral to compute the arc length L of the curve C: r (t) = <글t?, 4t, v2t) from the point…

A: length of arc given below..

Q: What does the arc length formula give for the length of the line y = x between x = 0 and x = a,…

A: line y = x between x = 0 and x = a

Q: compute the arc length function s(t) = | ||r'(u)|| du for the given value of a. %3D r(t) = (12, 212,…

A: Given that, rt=t2,2t2,t3a=0 From the given equation we get, ru=u2,2u2,u3 a=0

Q: Compute the line integral (х — y) dx + xe x dy, where C is the closed curve consisting of two line…

A: line integration

Q: Let f(x) = x³/2. Determine the length of the arc swept over x E la, b).

A:

Q: Find the arclength of the graph of the fun ction over the indicated inter val. (a) y = 2x3/2 + 3, 0…

A: Given : Functions and their interval (a) y = 2x3/2 + 3 , 0≤x≤9 (b) y = ln(cosx), [0, π3] (c) x =…

Q: 2. Write an arc length parameterization for the curve r(t) = cos ti + sin tj + 3t k ; 0<t

A:

Q: Let C be the curve in R³ parameterized by r(t) = (sin t, 2t, cos t) for 0< t< /2. (a) Compute the…

A: See the attachment

Q: Which one of the following is the parametric equa- tions of the line that is normal to the surface…

A:

Q: Let YR be the arc of the circle {|z| = R} that lies between the ray Arg(z) = T/4 and Arg(z) = 37/4.…

A: Contour integration

Q: Find the parametrization of the tangent line to the space curve r(t) = (e" , sin(t), (t + 1)-³) at t…

A: Given that  r(t)=(e^(4t),sin(t),(t+1)^(-3)) at t=0 We have to find out the parameterization of the…

Q: Find the arclength of y = sin (x) on the interval [0, a]. %3D

A:

Q: Compute the arc length function L = ||r'(u)|| du for r(t) = (9t2, 3t2, t), and a = 0.

A:

Q: Find the moving trihedral of the curve R(t) = (e^t)sin(t)i − (e^t)cos(t)j + (e^t)k at any t in the…

A:

Q: (a) Set up an integral for the length of the arc of the hyperbola xy = 1 from the point (1,1)  to…

A: Part (a)

Q: Let L be the tangent line to the hyperbola xy = 1 at x = a, where a &gt; 0. Show that the area of…

A:

Q: Let f(x,y) = 3x 2 y + e x+2xy . Determine the line integral of f (x,y) with respect to arc length…

A:

Q: 4. Find the exact arc length over the interval. b. x =y* from y = 1 to y = 4

A:

Q: Find the arc length of the following curve on the given interva x- 3r°, y=, 0sts v8 Ostsv8

A: Find your answer below

Q: Use Green's Theorem to evaluate F. dr, where F C consists of the arc of the curve y 1x x2 - from…

A:

Q: Let 3 x = cos' t, y = sin³ t, z = 7; 0 < t < r. Find the arc length of the parametric curve.

A:

Q: Calculate the arc length of the curve y over the given interval. y = In(cos x), 0 < x <T/4,

A: Over the interval a ≤ x ≤ b.

Q: Compute the arc length function L = | ||r(u)||du for r(t) = (16t/2, In(t), 32t), and a = 1. %3D la L…

A:

Q: Set up an integral to compute the arc length L of the curve C: r (t) = (t, 4t, V2t) %3D from the…

A: It can be found by integrating between limits of t= 0 to 1

Q: 4. Use the arc length formula to show that the length of a linear function f(x) = mx +c on the…

A:

Q: Q1: Consider the curve in E' parameterized by C:(t) = 1- Find the arc-length of the curve r(t)? 2-…

A: Given equation of the curve is rt=cos5t, sin5t, 12t

Q: If a(s) is a curve parametrized by arc length, prove that a"(s) is per- pendicular to a'(s). (ii)…

A: Given the curve

Q: Consider the space curve ř(t) = (8 sin(5t), 2/7 cos(5t), 6 cos(5t)). %3D a. Find the arc length…

A:

Q: Find the area of the Surface generated by revolving the given curve about the - axis while x is over…

A:

Q: Set up an integral to compute the arc length L of the curve C: r(t) = (, 4t, v2t) %3D from the point…

A: I am going to setup an integral to compute the arc length of the given curve using the required…

Q: Find the arc length of the curve y=x+7 on the interval [0,3] O153 O 90 O 45 O18

A: Given that y=x+7.

Q: Let C be the part of the space curve represented by r(t) = (1– e', 2e-, 2t) from t = –1 to t = 1.…

A:

Q: Find the arc length of the parametric curve. x = cos' t, y = sin° t, z = 2; 0 < t < T/2

A:

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: s) Evaluate the line itegral ( +2y + 2)dy – dz, where C is the arc of parabola z = 2+ y". from (2,0)…

A:

Q: Find the arc length from (x1, y1) to (x2, y2) on the graph of f(x) = mx + b.

A: Given Data The first point on the graph is (x1, y1). The second point on the graph is (x2, y2). The…

Q: (a) Compute the arc length of the portion of the curve r(t) = (2t,t², ln t) between the points (2,…

A: Step:- 1 Subpart:- (a) Since, we know Arc length (L) for any curve r(t); a≤t≤b is  L=∫t=abr'(t)dt…

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

A:

Q: Evaluate s(t) = J∞ |r'(u)||du for the Bernoulli spiral r(t) = (e'cos(3t), e' sin( 3t)). It is…

A: The given Bernoulli spiral is We have to find the integral, r'(u)=r'(t) Apply r'(t) in the above…

Q: Consider the curve r=[(e^(t))*cos(3t), (e^(t))*sin(3t), e^(t)] Compute the arclength function s(t):…

A: The arc length function is given as: st=∫atr'tdtrt=etcos3t,etsin3t,et  with initial point 0

Q: Let r(t) = -6t2 î+ (t² +3) ĵ + 7 k for t > 1. Reparameterize in terms of the arc-length parameter.

A:

Q: Let YR be the arc of the circle {|z| = R} that lies between the ray Arg(2) = T/4 and Arg(z) = 37/4.…

A:

Q: 3. a) Show that the length of the arc of the curve y=f(x) where f(x) = Insecx 0sxs is 4 In(1 + vz)…

A: L= integration of [1+{f'(x)}2] from a to b f(x) = ln sec x  f'(x) = tanx   Putting the value of…

Q: Which one of the following is the parametric equa- tions of the line that is normal to the surface…

A:

Q: Which one of the following is the parametric equa- tions of the line that is normal to the surface…

A: First we have to find partial differentiation with respect to x , y and z of function f such that-

Q: Compute the arc length function L = | ||r(u)||du for r(t) = (16t1/2, In(t), 32t), and a = 1. %3D %3D…

A:

Q: Set up an integral to compute the arc lengthL of the curve C: r(t) = (, 4t, v2t) from the point (0,…

A: Arc length

Vector Arithmetic

Vectors are those objects which have a magnitude along with the direction. In vector arithmetic, we will see how arithmetic operators like addition and multiplication are used on any two vectors. Arithmetic in basic means dealing with numbers. Here, magnitude means the length or the size of an object. The notation used is the arrow over the head of the vector indicating its direction.

Vector Calculus

Vector calculus is an important branch of mathematics and it relates two important branches of mathematics namely vector and calculus.