Question

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)

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
Let w = (x 2 -z)/ y4 , x = t3+7, y = cos(2t), z =...
Let w = (x 2 -z)/ y4 , x = t3+7, y = cos(2t), z = 4t. Use the Chain Rule to express dw/ dt in terms of t. Then evaluate dw/ dt at t = π/ 2
For the following equation x=2t^2,y=3t^2,z=4t^2;1 less or equal to t less or equal to 3 i)...
For the following equation x=2t^2,y=3t^2,z=4t^2;1 less or equal to t less or equal to 3 i) Write the positive vector tangent of the curve with parametric equations above. ii) Find the length function s(t) for the curve. iii) Write the position vector of s and verify by differentiation that this position vector in terms of s is a unit tangent to the curve.
Evaluate the line integral, where C is the given curve. xyeyz dy,   C: x = 2t,    y =...
Evaluate the line integral, where C is the given curve. xyeyz dy,   C: x = 2t,    y = 4t2,    z = 3t3,    0 ≤ t ≤ 1 C
Evaluate the line integral, where C is the given curve. xyeyz dy,   C: x = 2t,    y =...
Evaluate the line integral, where C is the given curve. xyeyz dy,   C: x = 2t,    y = 2t2,    z = 3t3,    0 ≤ t ≤ 1 C
Evaluate Integral (subscript c) z dx + y dy − x dz, where the curve C...
Evaluate Integral (subscript c) z dx + y dy − x dz, where the curve C is given by c(t) = t i + sin t j + cost k for 0 ≤ t ≤ π.
Consider the parametric curve defined by x = 3t − t^3 , y = 3t^2 ....
Consider the parametric curve defined by x = 3t − t^3 , y = 3t^2 . (a) Find dy/dx in terms of t. (b) Write the equations of the horizontal tangent lines to the curve (c) Write the equations of the vertical tangent lines to the curve. (d) Using the results in (a), (b) and (c), sketch the curve for −2 ≤ t ≤ 2.
Evaluate ∫ C 2 xyz d x + x^2 z dy + x^2 y d z...
Evaluate ∫ C 2 xyz d x + x^2 z dy + x^2 y d z over the path c ( t ) = ( t^2 , sin ⁡ ( π t /4 ) , e^(t^2 − 2t ) for 0 ≤ t ≤ 2.
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 ⊂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.
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. (a) (10 pts) Draw a sketch of the curve C determined by r(t). (b) (5 pts) Plot r(0) and label its endpoint P. (c) (10 pts) Plot the vector tangent to C at P . (d) (10 pts) Find the equation of the line tangent to C at P (you may give this parametrically or not). (e) (5 pts) Find the curvature K at P . (f) (5 pts) Find the radius of curvature ρ at P. (g) (5...
ADVERTISEMENT
Need Online Homework Help?

Get Answers For Free
Most questions answered within 1 hours.

Ask a Question
ADVERTISEMENT