Detailed Explanations for Calculus 2 Equations

The acceleration of an object after t seconds is given by the vector-valued function
$\vec{a} (t) = ⟨ \cos (8 t), \sin (8 t), - 5 ⟩$
If the object's initial position is $(- 9, - 3, 10)$ , and the object's initial velocity is $⟨ 1, 0, 1 ⟩$ , find a vector-valued function $\vec{r} (t)$ representing the object's position at time t.

kiki195ms 2021-11-27

Find parametric equations and a parameter interval for the motion of a particle that starts at $(a, 0)$ and traces the circle $x^{2} + y^{2} = a^{2}$ once counterclockwise

Travis Fogle 2021-11-27

Find parametric equations for the line through $(- 2, 0, 4)$ parallel to $v = 2 i + 4 j - 2 k$

balff1t 2021-11-27

Find two different parametric equations for rectangular equation.
$y = - 2 x + 4$

krypsojx 2021-11-27

Find parametric equations for the following curves. Include an interval for the parameter values. Answers are not unique.
The line segment starting at $P (- 1, - 3)$ and ending at $Q (6, - 16)$

danrussekme 2021-11-27

Find parametric equations for the given curve.
${(x + 9)}^{2} + {(y - 4)}^{2} = 49$

ffortunyu 2021-11-27

Find two different sets of parametric equations for a rectangular equation
$y - x^{2} - 3$

skeexerxo175o 2021-11-27

Determine whether the statement " The graph of the parametric equations $x = t^{2}$ and $y = t^{2}$ is the line $y = x^{'}$ '', is true or false. If it is false, expalain why or give an example that shows it is false.

Grady Turner 2021-11-27

Find the velocity and acceleration of the following vector-valued functions.
$r (t) = e^{- t} i + e^{t} j + 4 k$ at $t = 0$

jeliceg2 2021-11-27

Represent the plane curve by a vector-valued function. (There are many correct answers.)
$3 x + 4 y - 12 = 0$

cleritere39 2021-11-27

Compute the derivative of the vector-valued function $r (t) = ⟨ \sin 2 t, e t^{2} ⟩ .$

impresijuzj 2021-11-26

Domains Find the domain of the following vector-valued function.
$r (t) = \frac{2}{t - 1} i + \frac{3}{t + 2} j$

skomminbv 2021-11-26

Describe the motion of a particle when the tangential component of acceleration is 0.

grislingatb 2021-11-26

Represent the line segment from P(-2, -3, 8), Q(5, 1, -2) by a vector-valued function and by a set of parametric equations.

shelbs624c 2021-11-26

Discover a set of parametric equations of the line with the given characteristics. The line passes through the point. $(- 4, 5, 2)$ and is parallel to the xy-plane and the yz-plane

vomiderawo 2021-11-26

Consider the following function. (Let n be an arbitrary integer.)
$r (t) = \tan (t) i + j + k$
(a) Find the domain of r.
(b) Determine the interval(s) on which the function is continuous.

vousetmoiec 2021-11-26

Find the limit of the following vector-valued functions at the indicated value of t.
$lim_{t \to 4} ⟨ \sqrt{t - 3}, \frac{\sqrt{t -} 2}{t - 4}, \tan (\frac{π}{t}) ⟩$

inlays85k5 2021-11-26

Locate the open interval(s) on which the vectorvalued function's curve appears. $r () = 2 \cos^{3} i + 3 \sin^{3} j, 0 \leq\leq 2$ is smooth.

Halkadvalseln 2021-11-26

Derivatives of vector-valued functions
Differentiate the following function.
$r (t) = ⟨ 4, 3 \cos 2 t, 2 \sin 3 t ⟩$

zachutnat4o 2021-11-26

Find the velocity and acceleration of the following vector-valued functions.
$r (t) = t^{2} i + t^{4} j$ at $t = 1$

When you are dealing with any Calculus 2 homework, it is vital to have a look at the various questions and answers that will help you see whether you are correct in your approach to finding solutions. Even if you are dealing with analytical aspects of Calculus 2, it will be helpful as you are looking at provided equations and learn how the answers relate to original questions and problems specified.

Do not be afraid to take a look at the basic integration and related application if Calculus 2 does not sound clear or start with the Calculus 1 first.

Calculus 2

Calculus 2 Equations: Expert Solutions and More