Question

Let C ⊂R3 be the parametrized curve X(t) = (√2t, (2/3)t^(3/2), (2/3)t^(3/2) ), t ∈ [0,1]....

Let C ⊂R3 be the parametrized curve X(t) = (√2t, (2/3)t^(3/2), (2/3)t^(3/2) ), t ∈ [0,1].

(1) Compute the total length of C.

(2) Compute the curvature of C.

Homework Answers

Know the answer?
Your Answer:

Post as a guest

Your Name:

What's your source?

Earn Coins

Coins can be redeemed for fabulous gifts.

Not the answer you're looking for?
Ask your own homework help question
Similar Questions
Let C be the curve parametrized by r(t)=(t2+2)i+(1+t)j+2t^2k, with 0≤t≤. Consider the conservative vector field F=yz2i+xz2j+2xyzk,...
Let C be the curve parametrized by r(t)=(t2+2)i+(1+t)j+2t^2k, with 0≤t≤. Consider the conservative vector field F=yz2i+xz2j+2xyzk, Calculate ∫CF⋅dr
x=2−t, y=2t+1; −1≤t≤1 (a) Sketch the parametrized curve using any method, but you must explain your...
x=2−t, y=2t+1; −1≤t≤1 (a) Sketch the parametrized curve using any method, but you must explain your thinking in clear sentences, or show mathematical work. Pay attention to the given domain. (b) Choose one of (i) or (ii) below – only one will be graded. i. Set up and solve an integral for the arc length of this curve OR ii. Calculate the equation of the tangent line to this curve at some point (tell the reader which point you chose!)...
Find the length of the curve x = 3t^(2), y = 2t^(3) , 0 ≤ t...
Find the length of the curve x = 3t^(2), y = 2t^(3) , 0 ≤ t ≤ 1
For the given parametrized curve C, find the area above the x-y plane that is under...
For the given parametrized curve C, find the area above the x-y plane that is under C (using line integrals) C: r(t) = <3 cost, 3 sint, 2t> for 0 ≤ t ≤ 2π
Let C be the plane curve determined by the function r(t)=(3-t^2)i+(2t)j where -2<=t<=2. -Find T(t), T'(t),...
Let C be the plane curve determined by the function r(t)=(3-t^2)i+(2t)j where -2<=t<=2. -Find T(t), T'(t), the magnitude of T'(t), and N(t). Please show work, Thank you!
Let y = x 2 + 3 be a curve in the plane. (a) Give a...
Let y = x 2 + 3 be a curve in the plane. (a) Give a vector-valued function ~r(t) for the curve y = x 2 + 3. (b) Find the curvature (κ) of ~r(t) at the point (0, 3). [Hint: do not try to find the entire function for κ and then plug in t = 0. Instead, find |~v(0)| and dT~ dt (0) so that κ(0) = 1 |~v(0)| dT~ dt (0) .] (c) Find the center and...
Let C be a closed curve parametrized by r(t) = sin ti+cos tj with 0 ≤...
Let C be a closed curve parametrized by r(t) = sin ti+cos tj with 0 ≤ t ≤ 2π. Let F = yi − xj be a vector field. (a) Evaluate the line integral xyds. C (b) Find the circulation of F over C. (c) Find the flux of F over C.
A space curve C is parametrically parametrically defined by x(t)=e^t^(2) −10, y(t)=2t^(3/2) +10, z(t)=−π, t∈[0,+∞). (a)...
A space curve C is parametrically parametrically defined by x(t)=e^t^(2) −10, y(t)=2t^(3/2) +10, z(t)=−π, t∈[0,+∞). (a) What is the vector representation r⃗(t) for C ? (b) Is C a smooth curve? Justify your answer. (c) Find a unit tangent vector to C . (d) Let the vector-valued function v⃗ be defined by v⃗(t)=dr⃗(t)/dt Evaluate the following indefinite integral ∫(v⃗(t)×i^)dt. (cross product)
Find the length of the curve 1) x=2sin t+2t, y=2cos t, 0≤t≤pi 2) x=6 cos t,...
Find the length of the curve 1) x=2sin t+2t, y=2cos t, 0≤t≤pi 2) x=6 cos t, y=6 sin t, 0≤t≤pi 3) x=7sin t- 7t cos t, y=7cos t+ 7 t sin t, 0≤t≤pi/4
1. A plane curve has been parametrized with the following vector-valued function, r(t) = (t +...
1. A plane curve has been parametrized with the following vector-valued function, r(t) = (t + 2)i + (-2t2 + t + 1)j a. Carefully make 2 sketches of the plane curve over the interval . (5 pts) b. Compute the velocity and acceleration vectors, v(t) and a(t). (6 pts) c. On the 1st graph, sketch the position, velocity and acceleration vectors at t=-1. (5 pts) d. Compute the unit tangent and principal unit normal vectors, T and N at...
ADVERTISEMENT
Need Online Homework Help?

Get Answers For Free
Most questions answered within 1 hours.

Ask a Question
ADVERTISEMENT