Cram University
 
Username: Password:

Sign up (it's free!)   | |   forgot password?

 

Calc 3 10.8

 

<== Calculus 3
Number Question Answer
See the work
1. Find the arclength of the curve   \mathbf r(t) =  \langle 7 t^2, 2\sqrt{7}, for   1 &le t &le 9.
L =
L = 562.197
The work
2. Find the length of the given curve:

r(t) = ( 5t, -4sin(t), -4cos(t) )
where -5 &le t &le 2.

r(t) = 44.822
The work
3. Find the arclength of the curve \mathbf r(t) =  \langle 10 \sqrt2 t, e^{10 t}, e^{-10 t}
angle, 0 &le t &le 1
22026.466
The work
4. Consider the path \mathbf{r}(t) = (6 t, 3 t^2, 3\ln t) defined for t > 0.
Find the length of the curve between the points (6, 3, 0) and ( 30, 75, 3ln(5) ).
76.828
The work
5. Consider the curve \displaystyle  \mathbf{r} = 
(e^{5 t} \cos(-3 t), e^{5 t} \sin(-3 t), e^{5 t}).
Compute the arclength function s(t): (with initial point t=0).
The work
6. Starting from the point ( 1, -5, 3 ), reparametrize the curve
r(t) = ( 1 - t, -5 - 2t, 3 - t ) in terms of arclength.

r(t(s)) = (, ,)

The work
7. Starting from the point ( 1, 2, 4 ) reparametrize the curve

r(t) = ( 1 + t) i + ( 2 + 2t) j + ( 4 - 2t ) k
in terms of arclength.

r(t(s)) = i + j + k

1 + s/3i + 2 + 2s/3j + 4 - 2s/3k
The work