Question

A) Eliminate the parameter to obtain an equation in x and y calculator

B) Describe the curve and indicate the positive orientation.

x= 3 cos t, y=3 sin t; 0 <= t <= pi/2

Answer #1

Eliminate the parameter to find a Cartesian equation of the
curves:
a) x=3t+2,y=2t−3
b) x=21sin(t)−3,y=2cos(t)+5

Eliminate the parameter to find the Cartesian equation and
indicate in which direction the curve is being traversed. x =
2cost, y = 3sent with 0 <t <= 2π *
(x ^ 2) / 4 + (y ^ 2) / 9 = 1 counterclockwise
(x ^ 2) / 9 + (y ^ 2) / 4 = 1 counterclockwise
(x ^ 2) / 9 + (y ^ 2) / 4 = 1 clockwise
Other answer
(x ^ 2) / 4 +...

Eliminate the parameter to find the cartesian equation.
Then sketch the curve using t= 0, 90,180 degrees
Given; x= 2cost -2 and y= sint + 1

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.

Find the length of the curve
1) x=2sin t+2t, y=2cos t, 0≤t≤pi
2) x=6 cos t, y=6 sin t, 0≤t≤pi
3) x=7sin t- 7t cos t, y=7cos t+ 7 t sin t, 0≤t≤pi/4

1. Sketch the parametric curve [being careful with the domain
restriction]. Also, eliminate the parameter to find a single
equation for the points of the curve.
a. (x= sint, y= csct) 0 < t < ?/2
b. (x= et , y= e-2t ) t ∈ R
c. (x= 3cos2t, y= 2sin2t) ?/2 < t < ?
d. (x= t0.5 , y= 1-t) t > 0

a)Prove that the function
u(x, y) = x -y÷x+y
is harmonic and obtain a conjugate function v(x, y) such that
f(z) = u + iv is analytic.
b)Convert the integral
from 0 to 5 of (25-t²)^3/2 dt
into a Beta Function and evaluate the resulting function.
c)Solve the first order PDE
sin(x) sin(y)
∂u
∂x + cos(x) cos(y)
∂u
∂y = 0
such that u(x, y) = cos(2x), on x + y =
π
2

Determine the length of the graph of the given equation in the
indicated interval.
a) y= 4x^(3/2) from the point (0,0) to the point (1,4)
b) y^2 = x in the interval(range) [-1,1]
c) y= sin(x) in the interval (range) [0,pi]
d) y=ln(cos x) between the values x=0 and x= pi/2

Find an equation of the tangent line to the curve at the given
point. A) y = 6x + 3 cos x, P = (0, 3) B)y = 8 x cos x P = \(pi ,
-8 pi)
B)Find an equation of the tangent line to the curve at the given
point.
y = 8 x cos x
C)
If H(θ) = θ cos θ, find H'(θ) and H''(θ).
find H'(
θ)
and H"(θ)

1.) Let f ( x , y , z ) = x ^3 + y + z + sin ( x + z ) + e^( x
− y). Determine the line integral of f ( x , y , z ) with respect
to arc length over the line segment from (1, 0, 1) to (2, -1,
0)
2.) Letf ( x , y , z ) = x ^3 * y ^2 + y ^3 * z^...

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