- #1
Punchlinegirl
- 224
- 0
If someone could check my work and make sure I'm doing these problems right, I would really appreciate it.
1.Eliminate the parameter and obtain the standard form of the rectangular equation.
Circle: [tex] x= h + r cos \theta , y= k + r sin \theta [/tex]
[tex] (x-h/r)^2 + (y-k/r)^2 = 1[/tex]
2.Find the arc length of the given curve on the indicated interval.
[tex] x=t^2 +1, y=4t^3 + 3 [/tex]
[tex] 0 \leq t \leq -1 [/tex]
[tex] S= \int \sqrt (dx/dt)^2 + (dy/dt)^2 [/tex]
dx/dt= 2t, dy/dt= 12t^2
so i intregrated from -1 to 0, [tex] \int \sqrt 4t^2 +144t^2 dt [/tex]
using a u subsitution, I got [tex] 1/432(4+144t^2)^(3/2) [/tex]
Plugging in -1 and 0 gave me -4.15, which can't be right since it's talking about arclength..
3.Convert the rectangular equation to polar.
[tex] x^2 + y^2 - 2ax = 0 [/tex]
[tex] r^2 = 2ax [/tex]
[tex] r^2 / r cos \theta = 2a (r cos \theta)/ r cos \theta [/tex]
Solving for r gave me [tex] r= 2a cos \theta [/tex]
If these are wrong, any help would be appreciated. Thanks!
1.Eliminate the parameter and obtain the standard form of the rectangular equation.
Circle: [tex] x= h + r cos \theta , y= k + r sin \theta [/tex]
[tex] (x-h/r)^2 + (y-k/r)^2 = 1[/tex]
2.Find the arc length of the given curve on the indicated interval.
[tex] x=t^2 +1, y=4t^3 + 3 [/tex]
[tex] 0 \leq t \leq -1 [/tex]
[tex] S= \int \sqrt (dx/dt)^2 + (dy/dt)^2 [/tex]
dx/dt= 2t, dy/dt= 12t^2
so i intregrated from -1 to 0, [tex] \int \sqrt 4t^2 +144t^2 dt [/tex]
using a u subsitution, I got [tex] 1/432(4+144t^2)^(3/2) [/tex]
Plugging in -1 and 0 gave me -4.15, which can't be right since it's talking about arclength..
3.Convert the rectangular equation to polar.
[tex] x^2 + y^2 - 2ax = 0 [/tex]
[tex] r^2 = 2ax [/tex]
[tex] r^2 / r cos \theta = 2a (r cos \theta)/ r cos \theta [/tex]
Solving for r gave me [tex] r= 2a cos \theta [/tex]
If these are wrong, any help would be appreciated. Thanks!