Question

Letr(t)=(4t2+1)i+2tjfor−2≤t≤2. (a) (10 pts) Draw a sketch of the curve C determined by r(t). (b) (5...

Letr(t)=(4t2+1)i+2tjfor−2≤t≤2.

  1. (a) (10 pts) Draw a sketch of the curve C determined by r(t).

  2. (b) (5 pts) Plot r(0) and label its endpoint P.

  3. (c) (10 pts) Plot the vector tangent to C at P .

  4. (d) (10 pts) Find the equation of the line tangent to C at P (you may give this parametrically

    or not).

  5. (e) (5 pts) Find the curvature K at P .

  6. (f) (5 pts) Find the radius of curvature ρ at P.

  7. (g) (5 pts) Sketch the circle of curvature (the circle of best fit) at P.

Math   Calculus   
0 0
Add a commentTranscribed image text
Next >

Homework Answers

Answer #1

0 0
Know the answer?
Your Answer:

Post as a guest

Your Name:

What's your source?

Earn Coins

Coins can be redeemed for fabulous gifts.

Log In

Sign Up

Not the answer you're looking for?
Ask your own homework help question
Similar Questions
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...
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)
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 r(t) = < 2cost, 3t, 2sint > represent a parameterized curve. Find the: a) unit...
Let r(t) = < 2cost, 3t, 2sint > represent a parameterized curve. Find the: a) unit tangent vector b) unit normal vector c) curvature
The curve C is defined by the vector function: r(t) = 3ti + cos2tj + sin2tk....
The curve C is defined by the vector function: r(t) = 3ti + cos2tj + sin2tk. Find the Equations to the tangent line to the curve at the point P(0,1,0) corresponding to t=0. (please use a different parameter, say u, for tangent line)
Let r(t) = 1/2t ,4t^1/2 ,2t be a position function for some object. (a) (2 pts)...
Let r(t) = 1/2t ,4t^1/2 ,2t be a position function for some object. (a) (2 pts) Find the position of the object at t = 1. (b) (6 pts) Find the velocity of the object at t = 1. (c) (6 pts) Find the acceleration of the object at t = 1. (d) (6 pts) Find the speed of the object at t = 1. (e) (15 pts) Find the curvature K of the graph C determined by r(t) when...
Let C be the curve given by r(t) = <tcos(t), tsin(t), t>. a) Show that C...
Let C be the curve given by r(t) = <tcos(t), tsin(t), t>. a) Show that C lies on the cone x^2 + y^2 = z^2 and draw a rough sketch of C on the cone. b) Use a computer algebra system to plot the projections onto the xy- and yz-planes of the curve r(t) = <tcos(t), tsin(t).
Problem 5. Find the curvature of the curve R(t)=(t-sinh(t), 4cosh(t/2)), t > 0.
Problem 5. Find the curvature of the curve R(t)=(t-sinh(t), 4cosh(t/2)), t > 0.
Give your answer to two decimal places 1) Find the curvature of the curve r(t)=〈 5+...
Give your answer to two decimal places 1) Find the curvature of the curve r(t)=〈 5+ 5cos t , −5 ,−5sin t 〉 at the point t=11/12π 2) Find the curvature of the curve r(t)= 〈4+3t,5−5t,4+5t〉 the point t=5.
1) Find the curvature of the curve r(t)= 〈2cos(5t),2sin(5t),t〉 at the point t=0 Give your answer...
1) Find the curvature of the curve r(t)= 〈2cos(5t),2sin(5t),t〉 at the point t=0 Give your answer to two decimal places 2) Find the tangential and normal components of the acceleration vector for the curve r(t)=〈 t,5t^2,−5t^5〉 at the point t=2 a(2)=? →T +  →N
ADVERTISEMENT
Need Online Homework Help?

Get Answers For Free
Most questions answered within 1 hours.

Ask a Question
ADVERTISEMENT