Question

Graph the curve (? = −2 cos ? , ? = sin ? + sin 2?) . Then find the point where the curve crosses itself and find the equation of the two tangent lines at that point.

Answer #1

find the equation of the tangent lines at the point where the
curve crosses itself: x=cos^3(theta) y=sin^3(theta) y=t^2

Find the equation of the tangent line to the curve
r = 2 sin θ + cos θ
at the point
( x 0 , y 0 ) = ( − 1 , 3 )

1. Graph the curve given in parametric form by x = e t sin(t)
and y = e t cos(t) on the interval 0 ≤ t ≤ π2.
2. Find the length of the curve in the previous problem.
3. In the polar curve defined by r = 1 − sin(θ) find the points
where the tangent line is vertical.

1. Find the equation of the tangent line to the graph of ?2? −
5??2 + 6 = 0 at (3,1).
2.. Find the equation of the normal line to the graph of sin(??) =
? at the point (?/2 ,1).
3.. Find the equation of the tangent line to the graph of cos(??) =
? at the point (0.1)
Find implicit differentiation of dy/dx
a) xy=x+y
b) xcosy=y
c)x^3 +y^2=0

1) Sketch the graph?=? ,?=? +3,and include orientation.
2) Sketch the graph ? = sin ? , ? = sin2 ? + 3 and include
orientation.
3) Remove the parameter for ? = ? − 3, ? = ?2 + 3? − 2 and write
the corresponding
rectangular equation.
4) Remove the parameter for ? = 2 + 3 sin ? , ? = −1 + 3 cos ?
and write the corresponding rectangular equation.
5) Create a parameterization for...

Find the derivative of the parametric curve x=2t-3t2,
y=cos(3t) for 0 ≤ ? ≤ 2?.
Find the values for t where the tangent lines are horizontal on
the parametric curve. For the horizontal tangent lines, you do not
need to find the (x,y) pairs for these values of t.
Find the values for t where the tangent lines are vertical on
the parametric curve. For these values of t find the coordinates of
the points on the parametric curve.

Find an equation for the line tangent to the following curve at
the point (4,1).
1−y=sin(x+y^(2)−5)
Use symbolic notation and fractions where needed. Express the
equation of the tangent line in terms of y
and x.
equation:

7. For the parametric curve x(t) = 2 − 5 cos(t), y(t) = 1 + 3
sin(t), t ∈ [0, 2π) Part a: (2 points) Give an equation relating x
and y that represents the curve. Part b: (4 points) Find the slope
of the tangent line to the curve when t = π 6 . Part c: (4 points)
State the points (x, y) where the tangent line is horizontal

2)Find the slope of the tangent line to the curve r = sin (O) +
cos (O) at O = pi / 4 (O means theta)
3)Find the unit tangent vector at t = 0 for the curve r (t) =
4sen (t) i + 3tj + cos (t) k
4)A uniform cable measuring 40 feet is hung from the top of a
building. The cable weighs 60 pounds. How much work in foot-pounds
is required to climb 10 feet...

6.) Let ~r(t) =< 3 cos t, -2 sin t > for 0 < t < pi.
a) Sketch the curve. Make sure to pay attention to the parameter
domain, and indicate the orientation of the curve on your graph. b)
Compute vector tangent to the curve for t = pi/4, and sketch this
vector on the graph.

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