Recent questions in Parametric equations, polar coordinates, and vector-valued functions

Integral CalculusAnswered question

Isis Everett 2023-03-30

What is the area of the parallelogram with vertices A(-3, 0), B(-1, 5), C(7, 4), and D(5, -1)?

Integral CalculusAnswered question

Abril Huynh 2023-03-26

Find an equation equivalent to ${x}^{2}-{y}^{2}=4$ in polar coordinates.

Integral CalculusAnswered question

somi5fjt 2023-03-20

What is the exact length of the spiraling polar curve $r=5{e}^{2\theta}$ from 0 to $2\pi$?

Integral CalculusAnswered question

Teresa Manning 2023-03-14

What is the slope of the tangent line of $r=-2\mathrm{sin}\left(3\theta \right)-12\mathrm{cos}\left(\frac{\theta}{2}\right)$ at $\theta =\frac{-\pi}{3}$?

Integral CalculusAnswered question

Logan Glover 2023-03-02

How to find the length of the polar curve $r={\mathrm{cos}}^{3}\left(\frac{\theta}{3}\right)$?

Integral CalculusAnswered question

Jaslyn Gordon 2023-02-25

How to graph ${r}^{2}=\mathrm{cos}\left(2\theta \right)$?

Integral CalculusAnswered question

Damion Ellis 2023-02-15

Find arc length given $x=t\mathrm{sin}t$, $y=t\mathrm{cos}t$ and $0\le t\le 1$?

Integral CalculusAnswered question

YZ1FW5f4f 2023-02-13

Find the radius of convergence and interval of convergence. $\sum _{n=2}^{\infty}\frac{{(x+2)}^{n}}{{2}^{n}\mathrm{ln}n}$?

Integral CalculusAnswered question

Custodio88j 2023-02-13

How to find the exact length of the polar curve $r=3\mathrm{sin}\left(\theta \right)$ on the interval $0\le \theta \le \frac{\pi}{3}$?

Integral CalculusAnswered question

Heidy Haley 2023-02-12

How to find the slope of the tangent line to a polar curve?

Integral CalculusAnswered question

julioloupiasvfx 2023-02-02

How to graph $r\mathrm{sin}\left(\theta \right)=-1$?

Integral CalculusAnswered question

chichogpw4y 2023-02-01

How to graph the equation $r=1+\mathrm{cos}\left(\theta \right)$?

Integral CalculusAnswered question

ngukusizabw7 2023-01-26

What is a power series representation for $f\left(x\right)=\mathrm{ln}(1+x)$ and what is its radius of convergence?

Integral CalculusAnswered question

Jase Bentley 2023-01-10

Match the value of x in each case;

1. ${45}^{\circ}$

2. ${135}^{\circ}$

3. ${120}^{\circ}$

1. ${45}^{\circ}$

2. ${135}^{\circ}$

3. ${120}^{\circ}$

Integral CalculusAnswered question

Maxim Rosales 2022-12-23

How to find all points having an x coordinate of 3 whose distance from the point (-1, -4) is 5?

Integral CalculusAnswered question

intrigahQNn 2022-11-24

How to parameterize the paraboloid $z=9-{x}^{2}-{y}^{2}$? I know that I can parameterize it in cartesian coordinates as $r(x,y)=(x,y,9-{x}^{2}-{y}^{2})$ but I see in a book this parameterization of it that is $r(t)=(3cos(t),sin(t),0)$ with $0\le t\le 2\pi $ and I don't know how to deduce it.

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