MA 22S1
Assignment 1
Due 12-14 October 2015
Id:
22S1-f2015-1.m4,v 1.3 2015/10/11 19:11:54 john Exp john
1. Convert
x = 2t + 3,
y = 4t + 5
from paramatric to implicit form and
x + 2y = 3
from implicit to parametric.
2. Find the tangent lines to the parametric curve
x=
1 + t2
,
1 − t2
2t
1 − t2
at the points corresponding to the parameter values t = 0, t = 2 and
t = −3.
3. Find the length of the parametric curve
x=
1 + t2
,
1 − t2
y=
2t
,
1 − t2
1
1
− <t< .
2
2
Note: the integral you get is not one with elementary indefinite integral, so you can’t get a closed form solution. So just simplify the
integrand as much as you can, and leave it unintegrated, as in the last
arc length example I did in lecture.
1
Id:
22S1-f2015-1.m4,v 1.3 2015/10/11 19:11:54 john Exp john 2
4. Convert
r 4 sin2 (2θ) = 4
from polar to Cartesian coordinates and
1
1
y = x2 −
2
2
from Cartesian to polar coordinates.