Question

4)

Consider the polar curve *r=e ^{2theta}*

a) Find the parametric equations x = f(

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 area of the triangle PQR.

Answer #1

6) please show steps and explanation.
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 area of the triangle
PQR.

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.

Find the slope of the tangent line at each given polar curve at
each point specified by the values of θ.
r = 8 − sin(θ)
r = 1/θ
r = 9 + 4 cos(θ)
θ = π/3
θ = π
Thank you!

Consider the parametric curve given by the equations:
x = tsin(t) and y = t cos(t) for 0 ≤ t ≤ 1
(a) Find the slope of a tangent line to this curve when t =
1.
(b) Find the arclength of this curve

The polar curve r = 5sin3θ where 0 ≤ θ ≤ π. Find the area of one
loop of the curve. Find an equation for the line tangent which has
a positive slope to the curve at the pole.

Consider the parametric curve C deﬁned by the parametric
equations x = 3cos(t)sin(t) and y = 3sin(t). Find the expression
which represents the tangent of line C. Write the equation of the
line that is tangent to C at t = π/ 3.

Find parametric equations for the tangent line to the curve with
the given parametric equations at the specified point. x = 6
cos(t), y = 6 sin(t), z = 10 cos(2t); (3 3 , 3, 5)
x(t), y(t), z(t) = ??

Find parametric equations for the tangent line to the curve with
the given parametric equations at the specified point.
x =
e−5t
cos(5t), y =
e−5t
sin(5t), z =
e−5t; (1, 0, 1)

Find parametric equations for the tangent line to the curve with
the given parametric equations at the specified point.
x =
e−8t
cos(8t), y =
e−8t
sin(8t), z =
e−8t; (1, 0, 1)

Find the slope of the tangent line to the given polar curve at
the point specified by the value of θ.
r = 4 sin(θ), θ = π/6

ADVERTISEMENT

Get Answers For Free

Most questions answered within 1 hours.

ADVERTISEMENT

asked 14 minutes ago

asked 20 minutes ago

asked 25 minutes ago

asked 28 minutes ago

asked 35 minutes ago

asked 49 minutes ago

asked 56 minutes ago

asked 1 hour ago

asked 1 hour ago

asked 1 hour ago

asked 1 hour ago

asked 1 hour ago