Question

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 ? = ?2 whose orientation is right to left.

For problem 6-10 use the parametric equations ? = ?2 + 5,? = ?2 − 3? − 1 .

6) Find ??/??

7) Find ?2?/??2

8) Find the slope of the graph when ? = 2

9) Find the intervals on t for which the curve is concave up/down

10) Find the tangent line to the curve at the point (3,6)

For problem 11-14 use the parametric equations ? = ? , ? = 2? − 1 to answer a-e.

11) Find ??/??

12) Find ?2?/??2

13) Find the slope of the graph when ? = ln5

14) Find the intervals on which the curve is concave up/down

15) Find the arc length along the curve defined by ? = 2? − 3 , ? = ?2, on the interval of t values [0,3]. Give an exact answer.

16) Find different polar coordinates for the point (7, 3?/2 ) that satisfy the conditions set forth in

a) ?<0

b) ? < 0

c) any set of coordinates not already used

17) Convert (3, 4?/3 ) from polar to rectangular coordinates.

18) Convert (−7,7√3) from rectangular to polar coordinates.

19) Convert ? = ?2 its corresponding polar equation.

20) Convert ? sin ? = 7 its corresponding rectangular equation.

21) Convert tan ? = 7 its corresponding rectangular equation.

22) Use calculus to find the area of contained by ? = 3 + 3 sin
?

23) Use calculus to find the area inside a single petal of ? = 5
cos 2?

24) Use calculus to find the area inside ?=6sin? outside
?=2+2sin?

25) Use calculus to find the area of the inner figure eight of ? = sin (?/2)

Answer #1

Graph the polar equations: r = 1 + cos θ and r = 1 + sin θ. Find
where they intersect (in polar or rectangular coordinates) and set
up the integral to find the area inside both curves?

Sketch the graph of the polar equation r = 3 + 2 sin
theta

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.

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.

For the function ?(?) = ?^3 + 3x^2 + 1 determine
All intervals where the graph is concave up
All intervals where the graph is concave down
The coordinates of any points of inflection

Use a computer to graph the curve with the given vector
equation. Make sure you choose a parameter domain and view-points
that reveal the true nature of the curve
r(t)=< te^t, e^-t, t>
r(t) = < cos(8cos t) sint t , sin(8cos t) sin t, cos t
>
Please I need to graph in MATLAB these are problems for Stewart
Calculus 8th edition.
I don't not how to use matlab please I need the commands. Thank
you for your help!

2. Rotate the semicircle of radius 2 given by y = √(4 − x^2)
about the x-axis to generate a sphere of radius 2, and use this to
calculate the surface area of the sphere.
3. Consider the curve given by parametric equations x = 2
sin(t), y = 2 cos(t).
a. Find dy/dx
b. Find the arclength of the curve for 0 ≤ θ ≤ 2π.
4.
a. Sketch one loop of the curve r = sin(2θ) and find...

Find the exact length of the curve y=(x^3)/3 + 1/(4x) for
2≤x≤3
Conslder the curve deflned by x=t+1 and y=t^2. Find the
corresponding rectangular equation. Produce two graphs: one using
the rectangular equation and one using the parametric equations.
What are the differnce's between the graphs?
Please show work.

Analyze and sketch the graph of the function f(x) = (x −
4)2/3
(a) Determine the intervals on which f(x) is increasing /
decreasing
(b) Determine if any critical values correspond to a relative
maxima / minima
(c) Find possible inflection points
(d) Determine intervals where f(x) is concave up / down

a.
r=3 - 3cos(Θ), enter value for r on a table
when;
Θ=0, (π/3),(π/2),(2π/3),π,(4π/3),(3π/2),(5π/3) & 2π
b. plot points from a, sketch graph
c. use calculus to find slope at (π/2),(2π/3),(5π/3)
& 2π
d. find EXACT area inside the curve in 1st
quadrant

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