4)
Consider the polar curve r=e2theta
a) Find the parametric equations x = f(θ), y =...
4)
Consider the polar curve r=e2theta
a) Find the parametric equations x = f(θ), y =
g(θ) for this curve.
b) Find the slope of the line tangent to this curve when
θ=π.
6)
a)Suppose r(t) = < cos(3t), sin(3t),4t
>.
Find the equation of the tangent line to r(t)
at the point (-1, 0, 4pi).
b) Find a vector orthogonal to the plane through the points P
(1, 1, 1), Q(2, 0, 3), and R(1, 1, 2) and the...
1) Show that the formulas below represent the equation of a
circle.
x = h +...
1) Show that the formulas below represent the equation of a
circle.
x = h + r cos θ
y = k + r sin θ
2) Use the equations in the preceding problem to find a set of
parametric equations for a circle whose radius is r = 4 and whose
center is (-1,-2).
3) Plot each of the following points on the polar
plane. A(2, π/4), B(1, 3π/2), C(4, π)
Given any Cartesian coordinates, (x,y), there are polar
coordinates (?,?)(r,θ) with −?2<?≤?2.−π2<θ≤π2.
Find polar coordinates with...
Given any Cartesian coordinates, (x,y), there are polar
coordinates (?,?)(r,θ) with −?2<?≤?2.−π2<θ≤π2.
Find polar coordinates with −?2<?≤?2−π2<θ≤π2 for the
following Cartesian coordinates:
(a) If (?,?)=(18,−10)(x,y)=(18,−10) then
(?,?)=((r,θ)=( , )),
(b) If (?,?)=(7,8)(x,y)=(7,8) then
(?,?)=((r,θ)=( , )),
(c) If (?,?)=(−10,6)(x,y)=(−10,6) then
(?,?)=((r,θ)=( , )),
(d) If (?,?)=(17,3)(x,y)=(17,3) then
(?,?)=((r,θ)=( , )),
(e) If (?,?)=(−7,−5)(x,y)=(−7,−5) then
(?,?)=((r,θ)=( , )),
(f) If (?,?)=(0,−1)(x,y)=(0,−1) then (?,?)=((r,θ)=( ,))
a) Find the parametric equations for the circle centered at
(1,0) of radius 2 generated clockwise...
a) Find the parametric equations for the circle centered at
(1,0) of radius 2 generated clockwise starting from
(1+21/2 , 21/2). <---( one plus square
root 2, square root 2)
b) When given x(t) = tcost, y(t) = sint, 0 <_ t. Find dy/dx
as a function of t.
c) When given the parametric equations x(t) =
eatsin2*(pi)*t, y(t) = eatcos2*(pi)*t where a
is a real number. Find the arc length as a function of a for 0
<_ t...
1) x = t^3 + 1 , y = t^2 - t , Find an equation...
1) x = t^3 + 1 , y = t^2 - t , Find an equation of the tangent
to the curve at the point corresponding to t = 1
2) x = t^2 + 1 , y = 3t^2 + t ,Find
a) dy/dx ,
b) (d^2)y / dx^2
c) For which values of t is the curve concave upward?
3) sketch the curve: r = 1 - 3cos θ
4)A demand curve is given by p = 450/(x...