Parametric equations, polar coordinates, and vector-valued functions: Comprehensive Help

College
Calculus and Analysis
Integral Calculus
Parametric equations, polar coordinates, and vector-valued functions

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

enrotlavaec 2022-06-14

For $f (t) = (\frac{\cos t}{2}, \sin^{2} t)$ what is the distance between $f (\frac{π}{4})$ and $f (π)$ ?

gvaldytist 2022-06-14

How do you write a vector equation and a parametric equation for each line: the line through $A (3, 0, 4)$ and parallel to the x-axis?

Alannah Short 2022-06-14

How do you find the equations of tangent lines at the point where the curve crosses itself $x = t^{2} - t$ and $y = t^{3} - 3 t - 1$ ?

telegrafyx 2022-06-13

Parametric function
${\begin{cases} x (t) = \sin^{2} t \\ y (t) = \cot^{2} t \end{cases}$
I need to explore this function, but I can't find enough information in my language. I don't know the steps of exploring the parametric function and building the graphic. I'd like to learn how to explore such a function in parametric form.

Hailie Blevins 2022-06-13

What is the polar form of $(8, 3)$ ?

Roland Manning 2022-06-13

How do you rewrite the two parametric equations’ as one Cartesian equation $x = \sec (t), y = \tan (t), - \frac{π}{2} < t < \frac{π}{2} ?$

Santino Bautista 2022-06-13

Parametric function differentiation problem
$x = a \cos g (t) and y = b \sin g (t)$
$x y^{2} \frac{d^{2} y}{d x^{2}} = b^{2} \frac{d y}{d x}$

shmilybaby4i 2022-06-12

How do I find the 2 slopes at which this parametric function crosses itself?
$x (t) = 2 \sin (2 t) y (t) = 8 \sin (t)$

Sattelhofsk 2022-06-12

What is the distance between the following polar coordinates?:
$(3, \frac{7 π}{4}), (5, \frac{13 π}{8})$

Dale Tate 2022-06-11

How do you find parametric equations for the path of a particle that moves around the given circle $x^{2} + {(y - 2)}^{2} = 4$ clockwise, starting at (2, 2)?

Ezekiel Yoder 2022-06-11

What is the distance between the following polar coordinates?:
$(11, \frac{17 π}{12}), (4, \frac{π}{8})$

Gideon Adusei2022-06-10

Dwllane4 2022-06-10

Proof of the Envelope theorem for parametric functions in the Cartesian Plane
Given a family of parametric functions in the Cartesian Plane (f(t,k); g(t,k)), their envelope is found by solving the equation:
$\frac{\partial f}{\partial t} \frac{\partial g}{\partial k} - \frac{\partial f}{\partial k} \frac{\partial g}{\partial t} = 0$
How do I prove the above statement?

paris.richelle 2022-06-10

1)Find the local maximum and minimum values and saddle point(s) of the function. If you have three-dimensional graphing software, graph the function with a domain and viewpoint that reveal all the important aspects of the function. (Enter your answers as a comma-separated list. If an answer does not exist, enter DNE.)
f(x, y) = y^2 − 10y cos x, −1 ≤ x ≤ 7
2)Find the local maximum and minimum values and saddle point(s) of the function. If you have three-dimensional graphing software, graph the function with a domain and viewpoint that reveal all the important aspects of the function. (Enter your answers as a comma-separated list. If an answer does not exist, enter DNE.)
f(x, y) = 7(x^2 + y^2)e^(y2 − x2)

glycleWogry 2022-06-09

What is the polar form of $(- 10, 22)$ ?

Dale Tate 2022-06-09

Maximize this parametric function
For what values of $a > 0$ is
$\frac{1}{1 + | x |} + \frac{1}{1 + | x - a |}$
is maximized?

Mayra Berry 2022-06-08

Determine if a complex parametric function is analytic.
$z = x + i y$
$w = f (z) = u (x, y) + i v (x, y)$
$Analytic if: u_{x} = v_{y} and u_{y} = - v_{x}$
This is not to hard for most problems. However, what if z is in parametric form? For example,
$z (t) = \cos (t) + i \sin (t)$
Is it simply analytic if $u_{t} = v_{t}$ ?

Kendrick Hampton 2022-06-08

What is the distance between the following polar coordinates?: $(2, \frac{π}{4}), (5, \frac{5 π}{8})$

Jeffery Clements 2022-06-07

What does the Cartesian equation of a Parametric function tell us?

Those college students that must deal with parametric equations and complex tasks like polar coordinates and vector-valued functions know how important it is to find a reliable parametric equations solver who would help find the answers to the majority of questions.

The equations presented below have all the solutions already provided, which is good when you need an example or a starting point to continue with your Integral Calculus assignment. Remember to take a look at the notes that can be met at some Integral Calculus solutions that we have below.

Integral Calculus

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